Search

This article introduces a novel statistical framework for independent component analysis (ICA) of multivariate data. We propose methodology for estimating mutually independent components, and a versatile resampling-based procedure for inference, including misspecification testing. Independent components are estimated by combining a nonparametric probability integral transformation with a generalized nonparametric whitening method based on distance covariance that simultaneously minimizes all forms of dependence among the components. We prove the consistency of our estimator under minimal regularity conditions and detail conditions for consistency under model misspecification, all while placing assumptions on the observations directly, not on the latent components.Ustatistics of certain Euclidean distances between sample elements are combined to construct a test statistic for mutually independent components. The proposed measures and tests are based on both necessary and sufficient conditions for mutual independence. We demonstrate the improvements of the proposed method over several competing methods in simulation studies, and we apply the proposed ICA approach to two real examples and contrast it with principal component analysis. [ABSTRACT FROM AUTHOR]

The bipartite record linkage task consists of merging two disparate datafiles containing information on two overlapping sets of entities. This is nontrivial in the absence of unique identifiers and it is important for a wide variety of applications given that it needs to be solved whenever we have to combine information from different sources. Most statistical techniques currently used for record linkage are derived from a seminal article by Fellegi and Sunter in 1969. These techniques usually assume independence in the matching statuses of record pairs to derive estimation procedures and optimal point estimators. We argue that this independence assumption is unreasonable and instead target a bipartite matching between the two datafiles as our parameter of interest. Bayesian implementations allow us to quantify uncertainty on the matching decisions and derive a variety of point estimators using different loss functions. We propose partial Bayes estimates that allow uncertain parts of the bipartite matching to be left unresolved. We evaluate our approach to record linkage using a variety of challenging scenarios and show that it outperforms the traditional methodology. We illustrate the advantages of our methods merging two datafiles on casualties from the civil war of El Salvador. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

We present a unified approach to conjoint analysis models using a Bayesian framework. One data source is used to form a prior distribution for the partworths, whereas full-profile evaluations under a rating scale, ranking, discrete choice, or constant-sum scale constitute the likelihood data ('one model fits all'). Standard existing models for conjoint analysis, considered in the literature, become particular eases of the proposed specification, and explicit formulas for the gains of using multiple sources of data are presented. We demonstrate our method on a conjoint analysis dataset containing both self-explicated evaluations and constant-sum profile data on new automobiles originally collected and described by Krieger, Green, and Umesh. Our empirical findings are 'mixed' in that for some out-of-sample predictive measures our Bayesian approach is superior to using profile-only or self-explicated--only data, and for other measures it is not. Our findings suggest that the primary determinant as to whether sel f-explicated data add information above and beyond the profile data is the degree of incongruity between the calibration and validation data formats. Specifically, when the same type of data are collected for both sources, self-explicated data add less, and vice versa. A further contribution of our work (and one that is easily implemented, given the general nature of our approach) is that we take our data and fit constant sum, ranking, and binary choice models to it, allowing us to infer the 'change' in information when taking data and transforming its scale (a common practice). A simulation study indicates the viability of this approach. A simple Gibbs sampler simulation scheme adapted to the form of the outcome measure, using data augmentation and Metropolis sampling, is considered for inference under the model. KEY WORDS: Conjoint analysis, Gibbs sampler, Hierarchical Bayesian methods., 1. INTRODUCTION Over the last 20 years, conjoint analysis has evolved as the primary marketing research technique for measuring consumer trade-offs between multiattributed products and services. Introduced into marketing by [...]

The article offers the authors insight regarding the article of Fan, Han, and Gu which aims to offer an approximate expression for false discovery proportion in the case of multiple hypothesis testing problem. They note that a perturbation from normality can have significant ramifications for determining false discoveries proportion. Moreover, they address the impact of the assumption of normality on the methodology when used in motivating problem.

Ultra-high dimensional data often display heterogeneity due to either heteroscedastic variance or other forms of non-location-scale covariate effects. To accommodate heterogeneity, we advocate a more general interpretation of sparsity, which assumes that only a small number of covariates influence the conditional distribution of the response variable, given all candidate covariates; however, the sets of relevant covariates may differ when we consider different segments of the conditional distribution. In this framework, we investigate the methodology and theory of nonconvex, penalized quantile regression in ultra-high dimension. The proposed approach has two distinctive features: (1) It enables us to explore the entire conditional distribution of the response variable, given the ultra-high-dimensional covariates, and provides a more realistic picture of the sparsity pattern; (2) it requires substantially weaker conditions compared with alternative methods in the literature; thus, it greatly alleviates the difficulty of model checking in the ultra-high dimension. In theoretic development, it is challenging to deal with both the nonsmooth loss function and the nonconvex penalty function in ultra-high-dimensional parameter space. We introduce a novel, sufficient optimality condition that relies on a convex differencing representation of the penalized loss function and the subdifferential calculus. Exploring this optimality condition enables us to establish the oracle property for sparse quantile regression in the ultra-high dimension under relaxed conditions. The proposed method greatly enhances existing tools for ultra-high-dimensional data analysis. Monte Carlo simulations demonstrate the usefulness of the proposed procedure. The real data example we analyzed demonstrates that the new approach reveals substantially more information as compared with alternative methods. This article has online supplementary material. [ABSTRACT FROM AUTHOR]

This article proposes a bootstrap approach for assessing significance in the clustering of multidimensional datasets. The procedure compares two models and declares the more complicated model a better candidate if there is significant evidence in its favor. The performance of the procedure is illustrated on two well-known classification datasets and comprehensively evaluated in terms of its ability to estimate the number of components via extensive simulation studies, with excellent results. The methodology is also applied to the problem of k-means color quantization of several standard images in the literature and is demonstrated to be a viable approach for determining the minimal and optimal numbers of colors needed to display an image without significant loss in resolution. Additional illustrations and performance evaluations are provided in the online supplementary material. [ABSTRACT FROM AUTHOR]

This article develops a set of tools for smoothing and prediction with dependent point event patterns. The methodology is motivated by the problem of tracking weekly maps of violent crime events, but is designed to be straightforward to adapt to a wide variety of alternative settings. In particular, a Bayesian semiparametric framework is introduced for modeling correlated time series of marked spatial Poisson processes. The likelihood is factored into two independent components: the set of total integrated intensities and a series of process densities. For the former it is assumed that Poisson intensities are realizations from a dynamic linear model. In the latter case, a novel class of dependent stick-breaking mixture models are proposed to allow nonparametric density estimates to evolve in discrete time. This, a simple and flexible new model for dependent random distributions, is based on autoregressive time series of marginally beta random variables applied as correlated stick-breaking proportions. The approach allows for marginal Dirichlet process priors at each time and adds only a single new correlation term to the static model specification. Sequential Monte Carlo algorithms are described for online inference with each model component, and marginal likelihood calculations form the basis for inference about parameters governing temporal dynamics. Simulated examples are provided to illustrate the methodology, and we close with results for the motivating application of tracking violent crime in Cincinnati. [ABSTRACT FROM AUTHOR]

In this paper we offer a complete methodology of cumulative slicing estimation to sufficient dimension reduction. In parallel to the classical slicing estimation, we develop three methods that are termed, respectively, as cumulative mean estimation, cumulative variance estimation, and cumulative directional regression. The strong consistency for p= O( n1 / 2 / log n) and the asymptotic normality for p= o( n1 / 2) are established, where p is the dimension of the predictors and n is sample size. Such asymptotic results improve the rate p= o( n1 / 3) in many existing contexts of semiparametric modeling. In addition, we propose a modified BIC-type criterion to estimate the structural dimension of the central subspace. Its consistency is established when p= o( n1 / 2). Extensive simulations are carried out for comparison with existing methods and a real data example is presented for illustration. [ABSTRACT FROM AUTHOR]

In this paper we develop a nonparametric approach to clustering very high-dimensional data, designed particularly for problems where the mixture nature of a population is expressed through multimodality of its density. Therefore, a technique based implicitly on mode testing can be particularly effective. In principle, several alternative approaches could be used to assess the extent of multimodality, but in the present problem the excess mass method has important advantages. We show that the resulting methodology for determining clusters is particularly effective in cases where the data are relatively heavy tailed or show a moderate to high degree of correlation, or when the number of important components is relatively small. Conversely, in the case of light-tailed, almost-independent components when there are many clusters, clustering in terms of modality can be less reliable than more conventional approaches. This article has supplementary material online. [ABSTRACT FROM AUTHOR]

The minimal depth of a maximal subtree is a dimensionless order statistic measuring the predictiveness of a variable in a survival tree. We derive the distribution of the minimal depth and use it for high-dimensional variable selection using random survival forests. In big p and small n problems (where p is the dimension and n is the sample size), the distribution of the minimal depth reveals a “ceiling effect” in which a tree simply cannot be grown deep enough to properly identify predictive variables. Motivated by this limitation, we develop a new regularized algorithm, termed RSF-Variable Hunting. This algorithm exploits maximal subtrees for effective variable selection under such scenarios. Several applications are presented demonstrating the methodology, including the problem of gene selection using microarray data. In this work we focus only on survival settings, although our methodology also applies to other random forests applications, including regression and classification settings. All examples presented here use the R-software package randomSurvivalForest. [ABSTRACT FROM AUTHOR]

In this paper we develop multivariate outlier tests based on the high-breakdown Minimum Covariance Determinant estimator. The rules that we propose have good performance under the null hypothesis of no outliers in the data and also appreciable power properties for the purpose of individual outlier detection. This achievement is made possible by two orders of improvement over the currently available methodology. First, we suggest an approximation to the exact distribution of robust distances from which cut-off values can be obtained even in small samples. Our thresholds are accurate, simple to implement and result in more powerful outlier identification rules than those obtained by calibrating the asymptotic distribution of distances. The second power improvement comes from the addition of a new iteration step after one-step reweighting of the estimator. The proposed methodology is motivated by asymptotic distributional results. Its finite sample performance is evaluated through simulations and compared to that of available multivariate outlier tests. [ABSTRACT FROM AUTHOR]

The statistical analysis of functional data is a growing need in many research areas. In particular, a robust methodology is important to study curves, which are the output of many experiments in applied statistics. As a starting point for this robust analysis, we propose, analyze, and apply a new definition of depth for functional observations based on the graphic representation of the curves. Given a collection of functions, it establishes the "centrality" of an observation and provides a natural center-outward ordering of the sample curves. Robust statistics, such as the median function or a trimmed mean function, can be defined from this depth definition. Its finite-dimensional version provides a new depth for multivariate data that is computationally feasible and useful for studying high-dimensional observations. Thus, this new depth is also suitable for complex observations such as microarray data, images, and those arising in some recent marketing and financial studies. Natural properties of these new concepts are established and the uniform consistency of the sample depth is proved. Simulation results show that the corresponding depth based trimmed mean presents better performance than other possible location estimators proposed in the literature for some contaminated models. Data depth can be also used to screen for outliers. The ability of the new notions of depth to detect "shape" outliers is presented. Several real datasets are considered to illustrate this new concept of depth, including applications to microarray observations, weather data, and growth curves. Finally, through this depth, we generalize to functions the Wilcoxon rank sum test. It allows testing whether two groups of curves come from the same population. This functional rank test when applied to children growth curves shows different growth patterns for boys and girls. [ABSTRACT FROM AUTHOR]

It is often of interest to recover derivatives of a sample of random functions from sparse and noise-contaminated measurements, especially when the dynamics of underlying processes is of interest. We propose a novel approach based on estimating derivatives of eigenfunctions and expansions of random functions into their eigenfunctions to obtain a representation for derivatives. In combination with estimates for functional principal component scores for sparse data, this leads to a viable solution of the challenging problem to recover derivatives for sparsely observed functions. We establish consistency results and demonstrate in simulations that the method is superior to alternative approaches (derivative estimation with random effects models based on B-spline bases, kernel smoothing, smoothing splines, or P-splines). Our study is motivated by an analysis of bidding histories for eBay auctions, for which bids are typically very sparse in the middle and somewhat more frequent near the beginning and end of an auction. We demonstrate the estimation of derivatives of price curves for individual auctions from the sparsely observed bidding histories and also derive a model-free first-order differential equation that applies in the case of Gaussian processes. This provides a data-driven dynamic model that we use to elucidate auction dynamics. [ABSTRACT FROM AUTHOR]

Kinetic analysis is used to extract metabolic information from dynamic positron emission tomography (PET) uptake data. The theory of indicator dilutions, developed in the seminal work of Meier and Zierler (1954), provides a probabilistic framework for representation of PET tracer uptake data in terms of a convolution between an arterial input function and a tissue residue. The residue is a scaled survival function associated with tracer residence in the tissue. Nonparametric inference for the residue, a deconvolution problem, provides a novel approach to kinetic analysis—critically one that is not reliant on specific compartmental modeling assumptions. A practical computational technique based on regularized cubic B-spline approximation of the residence time distribution is proposed. Nonparametric residue analysis allows formal statistical evaluation of specific parametric models to be considered. This analysis needs to properly account for the increased flexibility of the nonparametric estimator. The methodology is illustrated using data from a series of cerebral studies with PET and fluorodeoxyglucose (FDG) in normal subjects. Comparisons are made between key functionals of the residue, tracer flux, flow, etc., resulting from a parametric (the standard two-compartment of Phelps et al. 1979) and a nonparametric analysis. Strong statistical evidence against the compartment model is found. Primarily these differences relate to the representation of the early temporal structure of the tracer residence—largely a function of the vascular supply network. There are convincing physiological arguments against the representations implied by the compartmental approach but this is the first time that a rigorous statistical confirmation using PET data has been reported. The compartmental analysis produces suspect values for flow but, notably, the impact on the metabolic flux, though statistically significant, is limited to deviations on the order of 3%-4%. The general advantage of the nonparametric residue analysis is the ability to provide a valid kinetic quantitation in the context of studies where there may be heterogeneity or other uncertainty about the accuracy of a compartmental model approximation of the tissue residue. [ABSTRACT FROM AUTHOR]

We analyze data collected in a somatic embryogenesis experiment carried out on Zea mays at Iowa State University. The main objective of the study was to identify the set of genes in maize that actively participate in embryo development. Embryo tissue was sampled and analyzed at various time periods and under different mediums and light conditions. As is the case in many microarray experiments, the operator scanned each slide multiple times to find the slide-specific 'optimal' laser and sensor settings. The multiple readings of each slide are repeated measurements on different scales with differing censoring; they cannot be considered to be replicate measurements in the traditional sense. Yet it has been shown that the choice of reading can have an impact on genetic inference. We propose a hierarchical modeling approach to estimating gene expression that combines all available readings on each spot and accounts for censoring in the observed values. We assess the statistical properties of the proposed expression estimates using a simulation experiment. As expected, combining all available scans using an approach with good statistical properties results in expression estimates with noticeably lower bias and root mean squared error relative to other approaches that have been proposed in the literature, Inferences drawn from the somatic embryogenesis experiment, which motivated this work changed drastically when data were analyzed using the standard approaches or using the methodology we propose. [ABSTRACT FROM AUTHOR]

Allegations of racially biased policing are a contentious issue in many communities. Processes that flag potential problem officers have become a key component of risk management systems at major police departments. We present a statistical method to flag potential problem officers by blending three methodologies that are the focus of active research efforts: propensity score weighting, doubly robust estimation, and false discovery rates. Compared with other systems currently in use, the proposed method reduces the risk of flagging a substantial number of false positives by more rigorously adjusting for potential confounders and by using the false discovery rate as a measure to flag officers. We apply the methodology to data on 500,000 pedestrian stops in New York City in 2006. Of the nearly 3,000 New York City Police Department officers regularly involved in pedestrian stops, we flag 15 officers who stopped a substantially greater fraction of black and Hispanic suspects than our statistical benchmark predicts. [ABSTRACT FROM AUTHOR]

We describe a class of log-linear models for the detection of interactions in high-dimensional genomic data. This class of models leads to a Bayesian model selection algorithm that can be applied to data that have been reduced to contingency tables using ranks of observations within subjects, and discretization of these ranks within gene/network components. Many normalization issues associated with the analysis of genomic data are thereby avoided. A prior density based on Ewens' sampling distribution is used to restrict the number of interacting components assigned high posterior probability, and the calculation of posterior model probabilities is expedited by approximations based on the likelihood ratio statistic. Simulation studies are used to evaluate the efficiency of the resulting algorithm for known interaction structures. Finally, the algorithm is validated in a microarray study for which it was possible to obtain biological confirmation of detected interactions. [ABSTRACT FROM AUTHOR]

There has been a recent surge of interest in modeling and methods for analyzing recurrent events data with risk of termination dependent on the history of the recurrent events. To aid future users in understanding the implications of modeling assumptions and modeling properties, we review the state-of-the-art statistical methods and present novel theoretical properties, identifiability results, and practical consequences of key modeling assumptions of several fully specified stochastic models. After introducing stochastic models with 2 noninformative termination process, we focus on a class of models that allows both negative and positive association between the risk of termination and the rate of recurrent events through a frailty variable. We also discuss the relationship, as well as the major differences between these models in terms of their motivations and physical interpretations. We discuss associated Bayesian methods based on Markov chain Monte Carlo tools, and novel model diagnostic tools to perform inference based on fully specified models. We demonstrate the usefulness of the current methodology through an analysis of a data set from a clinical trial. Finally, we explore possible future extensions and limitations of the methodology. [ABSTRACT FROM AUTHOR]

Quantile regression offers great flexibility in assessing covariate effects on event times, thereby attracting considerable interests in its applications in survival analysis. But currently available methods often require stringent assumptions or complex algorithms. In this article we develop a new quantile regression approach for survival data subject to conditionally independent censoring. The proposed martingale-based estimating equations naturally lead to a simple algorithm that involves minimizations only of L1-type convex functions. We establish uniform consistency and weak convergence of the resultant estimators. We develop inferences accordingly, including hypothesis testing, second-stage inference, and model diagnostics. We evaluate the finite-sample performance of the proposed methods through extensive simulation studies. An analysis of a recent dialysis study illustrates the practical utility of our proposals. [ABSTRACT FROM AUTHOR]

We propose a unified framework for testing various assumptions commonly made for covariance functions of stationary spatio-temporal random fields. The methodology is based on the asymptotic normality of space-time covariance estimators. We focus on tests for full symmetry and separability in this article, but our framework naturally covers testing for isotropy and Taylor's hypothesis. Our test successfully detects the asymmetric and nonseparable features in two sets of wind speed data. We perform simulation experiments to evaluate our test and conclude that our method is reliable and powerful for assessing common assumptions on space-time covariance functions. [ABSTRACT FROM AUTHOR]

Surface estimation is important in many applications. When conventional smoothing procedures (e.g., running averages, local polynomial kernel smoothing procedures, smoothing spline procedures) are used for estimating jump surfaces from noisy data, jumps are blurred at the same time when noise is removed. In recent years, new smoothing methodologies have been proposed in the statistical literature for detecting jumps in surfaces and for estimating jump surfaces with jumps preserved. We provide a review of these methodologies. Because a monochrome image can be considered a jump surface of the image intensity function, with jumps at the outlines of objects, edge detection and image restoration problems in image processing are closely related to the jump surface estimation problem in statistics. We also review major methodologies on edge detection and image restoration, and discuss connections and differences among these methods and related methods in the statistical literature. [ABSTRACT FROM AUTHOR]

Optimal incomplete block designs are pursued through the E criterion of minimizing maximal variance. Methodology is developed for design choice based on graphs and an extensive catalog of downloadable designs is complied. Along with the general methodology, a near complete solution for E-optimal block designs is provided for up to 15 treatments. E optimality is revealed to be a flexible criterion that, depending on the application, can offer many choices for good designs. [ABSTRACT FROM AUTHOR]

Binary support vector machines (SVMs) have been proven to deliver high performance. In multiclass classification, however, issues remain with respect to variable selection. One challenging issue is classification and variable selection in the presence of variables in the magnitude of thousands, greatly exceeding the size of training sample. This often occurs in genomics classification. To meet the challenge, this article proposes a novel multiclass support vector machine, which performs classification and variable selection simultaneously through an LI-norm penalized sparse representation. The proposed methodology, together with the developed regularization solution path, permits variable selection in such a situation. For the proposed methodology, a statistical learning theory is developed to quantify the generalization error in an attempt to gain insight into the basic structure of sparse learning, permitting the number of variables to greatly exceed the sample size. The operating characteristics of the methodology are examined through both simulated and benchmark data and are compared against some competitors in terms of accuracy of prediction. The numerical results suggest that the proposed methodology is highly competitive. [ABSTRACT FROM AUTHOR]

Multiple hypothesis testing and clustering have been the subject of extensive research in high-dimensional inference, yet these problems usually have been treated separately. By defining true clusters in terms of shared parameter values, we could improve the sensitivity of individual tests, because more data bearing on the same parameter values are available. We develop and evaluate a hybrid methodology that uses clustering information to increase testing sensitivity and accommodates uncertainty in the true clustering. To investigate the potential efficacy of the hybrid approach, we first study a stylized example in which each object is evaluated with a standard z score but different objects are connected by shared parameter values. We show that there is increased testing power when the clustering is estimated sufficiently well. We next develop a model-based analysis using a conjugate Dirichlet process mixture model. The method is general, but for specificity we focus attention on microarray gene expression data, to which both clustering and multiple testing methods are actively applied. Clusters provide the means for sharing information among genes, and the hybrid methodology averages over uncertainty in these clusters through Markov chain sampling. Simulations show that the hybrid method performs substantially better than other methods when clustering is heavy or moderate and performs well even under weak clustering. The proposed method is illustrated on microarray data from a study of the effects of aging on gene expression in heart tissue. [ABSTRACT FROM AUTHOR]

Regression is a useful tool for studying association between an outcome variable and its covariates. In a classical linear regression model, the outcome's expectation is usually a function of the covariates and some regression parameters, and the underlying distribution is often normal. In this article we propose a new class of additive expectancy regression models in which the outcomes tend to be positively skewed. In the new regression models, regression parameters are practically meaningful and also useful with inferences on the means of skewed outcomes. Parametric and semiparametric methods are developed for model estimation and inferences. Model-based prediction and model adequacy assessment are discussed. The proposed methodologies are demonstrated by two real data analyses. [ABSTRACT FROM AUTHOR]

The problem considered involves forecasting the future costs of hard drives of various capacities and speeds of revolution or, more generally, forecasting the future costs of various quantifiably different versions of a commodity that is subject to technological advance. In the primary development, it is supposed that the data consist of past and present costs. A model is proposed in which the past. present, and future costs of each version are related with each other and also with the costs of the other versions. The model encompasses a stochastic version of an empirical relationship known as Moore's law. A forecasting methodology was developed by adopting a Bayesian approach and taking the prior distribution to be of a relatively tractable them. An implementation of the Gibbs sampler was devised top making draws from the posterior distribution of the future costs: the forecasts are based on those draws. The proposed methodology was used to obtain forecasts retrospectively from data accumulated (over a 5-year period) on the quarterly costs of hard drives. The accuracy of the longer-term forecasts compared favorably with those of certain benchmark forecasts, whereas the accuracy of the shorter-term forecasts compared less favorably. Greater accuracy can be achieved through enhancements to the proposed methodology that provide for the use of supplementary information (i.e., information that is relevant but not fully reflected in the past and present costs). [ABSTRACT FROM AUTHOR]

An increasing number of statistical problems arise in connection with functional calibration. In each case, inexpensive indirect data in a particular context are combined with direct expensive-to-acquire data from different but related settings to estimate quantities in the former case. Sometimes (e.g., in chemometrics problems where spectroscopic calibration is used) the indirect data are functional. But more commonly, they are scalar or vector-valued, and the functional component is the quantity that we wish to estimate. The problem treated here is of the latter type. We observe data that give us access to the distribution of U given V, and from these and data on U, we wish to estimate the density of V. The motivating real datasets are of age and covariate information in fish populations. We suggest two methodologies, each of which is based on transforming the problem to one involving inversion of a symmetric linear operator. Our techniques have connections to methods for functional data analysis and for a variety of mixture and deconvolution problems, as well as to calibration techniques. [ABSTRACT FROM AUTHOR]

Discrimination of time series is an important practical problem with applications in various scientific fields. We propose and study a novel approach to this problem. Our approach is applicable to cases where time series in different categories have a different "shape." Although based on the idea of feature extraction, our method is not distance-based, and as such does not require aligning the time series. Instead, features are measured for each time series, and discrimination is based on these individual measures. An AR process with a time-varying variance is used as an underlying model. Our method then uses shape measures or, better, measures of concentration of the variance function, as a criterion for discrimination. It is this concentration aspect or shape aspect that makes the approach intuitively appealing. We provide some mathematical justification for our proposed methodology, as well as a simulation study and an application to the problem of discriminating earthquakes and explosions. [ABSTRACT FROM AUTHOR]

We develop a procedure for analyzing multivariate nonstationary time series using the SLEX library (smooth localized complex exponentials), which is a collection of bases, each basis consisting of waveforms that are orthogonal and time-localized versions of the Fourier complex exponentials. Under the SLEX framework, we build a family of multivariate models that can explicitly characterize the time- varying spectral and coherence properties. Every model has a spectral representation in terms of a unique SLEX basis. Before selecting a model, we first decompose the multivariate time series into nonstationary components with uncorrelated (nonredundant) spectral information. The best SLEX model is selected using the penalized log energy criterion, which we derive in this article to be the Kullback-Leibler distance between a model and the SLEX principal components of the multivariate time series. The model selection criterion takes into account all of the pairwise cross-correlation simultaneously in the multivariate time series. The proposed SLEX analysis gives results that are easy to interpret, because it is an automatic time-dependent generalization of the classical Fourier analysis of stationary time series. Moreover, the SLEX method uses computationally efficient algorithms and hence is able to provide a systematic framework for extracting spectral features from a massive dataset. We illustrate the SLEX analysis with an application to a multichannel brain wave dataset recorded during an epileptic seizure. [ABSTRACT FROM AUTHOR]

For the common binary response model, we propose a direct method for the nonparametric estimation of the effective dose level. The estimator is obtained by the composition of a nonparametric estimate of the quantile response curve and a classical density estimate. The new method yields a simple and reliable monotone estimate of the effective dose-level curve α ↠ EDα and is appealing to users of conventional smoothing methods as kernel estimators, local polynomials, series estimators, or smoothing splines. Moreover, it is computationally very efficient, because it does not require a numerical inversion of a monotonized estimate of the quantile dose-response curve. We prove asymptotic normality of the new estimate and compare it with an available alternative estimate (based on a monotonized nonparametric estimate of the dose-response curve and calculation of the inverse function) by means of a simulation study. [ABSTRACT FROM AUTHOR]

Over the last decade, technological advances have generated an explosion of data with substantially smaller sample size relative to the number of covariates (p≫u). A common goal in the analysis of such data involves uncovering the group structure of the observations and identifying the discriminating variables. In this article we propose a methodology for addressing these problems simultaneously. Given a set of variables, we formulate the clustering problem in terms of a multivariate normal mixture model with an unknown number of components and use the reversible-jump Markov chain Monte Carlo technique to define a sampler that moves between different dimensional spaces. We handle the problem of selecting a few predictors among the prohibitively vast number of variable subsets by introducing a binary exclusion/inclusion latent vector, which gets updated via stochastic search techniques. We specify conjugate priors and exploit the conjugacy by integrating out some of the parameters. We describe strategies for posterior inference and explore the performance of the methodology with simulated and real datasets. [ABSTRACT FROM AUTHOR]

Here we present a novel method for modeling stationary time series. Our approach is to construct the model with a specified marginal family and build the dependence structure around it. We show that the resulting time series is linear with a simple autocorrelation structure. We construct models that parallel existing structures, namely state-space models, autoregressive conditional heteroscedasticity (ARCH) models, and generalized ARCH models. We use Bayesian techniques to estimate the resulting models. We also demonstrate that the models perform well compared with competing methods for the applications considered, count models and volatility models. [ABSTRACT FROM AUTHOR]

Studies that estimate the effects of exposure to a possibly harmful agent often compare exposed subjects who received varied doses with matched controls who received zero dose. If the doses are measured with error, then one may wish to use the fallible doses to estimate a linear relationship between the unobserved true dose and the observed response. If one is willing to assume that the dose errors for exposed subjects are symmetrically distributed about 0-that is, the dose errors are pure errors and not, say, systematic underreporting of exposure-then the presence of zero-dose controls is all that is needed to obtain exact, distribution-free confidence intervals and tests, and consistent point estimates. The method is simpler for matched pairs than for matched sets with two or more matched subjects, and it is illustrated using two studies, one of each kind. With matched pairs, as in this first example, the method uses Wilcoxon's signed rank test as the basis for inference. When there are several zero-dose controls matched to each exposed subject, the familiar null distribution of the signed rank statistic is no longer applicable because of dependence within matched sets, so the appropriate exact distribution and large-sample approximation are developed. [ABSTRACT FROM AUTHOR]

In this article we study the semiparametric proportional odds model with random effects for correlated, right-censored failure time data. We establish that the maximum likelihood estimators for the parameters of this model are consistent and asymptotically Gaussian. Furthermore, the limiting variances achieve the semiparametric efficiency bounds and can be consistently estimated. Simulation studies show that the asymptotic approximations are accurate for practical sample sizes and that the efficiency gains of the proposed estimators over those of Cai, Cheng, and Wei can be substantial. A real example is provided to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

Truncated survival data arise when the failure time is observed only if it falls within a subject-specific truncating set. Most analysis methods rely on the key assumption of quasi-independence, that is, factorization of the joint density of failure and truncation times into a product proportional to the individual densities in the observable region. Unlike independence of failure time and censoring time, quasi-independence can be tested. Tests of quasi-independence are available for one-sided truncation and for truncation that depends on a measured covari-ate, but not for more complex truncation schemes. Here tests of quasi-independence based on a multivariate conditional Kendall's tau are proposed for doubly truncated data, bivariate left-truncated data, and other forms of truncated survival data that arise when initiating or terminating event times are interval-censored. Asymptotic properties under the null are derived. The tests are illustrated using several real datasets and evaluated via simulation. [ABSTRACT FROM AUTHOR]

Many biomedical observational studies attempt to relate a continuous outcome to an environmental exposure and other important covariates. If the outcome is easier or cheaper to measure relative to the exposure of interest, then the outcome may be observed for every member of a finite-study population, whereas exposure measurements may be obtained only for a relatively small subsample of this population. Rather than selecting a simple random subsample of individuals for exposure measurement, investigators may attempt to enhance study efficiency by allowing the selection probabilities to depend on the observed outcomes; we refer to such sampling schemes as outcome-dependent sampling (ODS). Standard estimation methods that ignore the ODS design will yield biased and inconsistent parameter estimates. Furthermore, it is generally desirable to use estimators that incorporate all available data as analyses restricted to subjects with complete information are inefficient. To this end, we extend an estimated likelihood method, originally developed for discrete outcome measurement error problems in which accurate exposure measurements are made only for a simple random "validation" sample, to allow for continuous outcomes and ODS designs. We derive the asymptotic properties of the proposed estimator and use simulated data to show that the asymptotic results closely approximate the finite-sample properties in samples of moderate size. We also use simulated data to compare the performance of our proposed estimator with that of existing methods applicable to the ODS problem. [ABSTRACT FROM AUTHOR]

A family of dimension-reduction methods, the inverse regression (1R) family, is developed by minimizing a quadratic objective function. An optimal member of this family, the inverse regression estimator (IRE), is proposed, along with inference methods and a computational algorithm. The IRE has at least three desirable properties: (1) Its estimated basis of the central dimension reduction subspace is asymptotically efficient, (2) its test statistic for dimension has an asymptotic chi-squared distribution, and (3) it provides a chi-squared test of the conditional independence hypothesis that the response is independent of a selected subset of predictors given the remaining predictors. Current methods like sliced inverse regression belong to a suboptimal class of the IR family. Comparisons of these methods are reported through simulation studies. The approach developed here also allows a relatively straightforward derivation of the asymptotic null distribution of the test statistic for dimension used in sliced average variance estimation. [ABSTRACT FROM AUTHOR]

Inverse regression methods facilitate dimension-reduction analyses of high-dimensional data by extracting a small number of factors that are linear combinations of the original predictor variables. But the estimated factors may not lend themselves readily to interpretation consistent with prior information. Our approach to solving this problem is to first incorporate prior information via theory- or data-driven constraints on model parameters, and then apply the proposed method, constrained inverse regression (CIR), to extract factors that satisfy the constraints. We provide chi-squared and r tests to assess the significance of each factor and its estimated coefficients, and we also generalize CIR to other inverse regression methods in situations where both dimension reduction and factor interpretation are important. Finally, we investigate CIR's small-sample performance, test data-driven constraints, and present a marketing example to illustrate its use in discovering meaningful factors that influence the desirability of brand logos. [ABSTRACT FROM AUTHOR]

We propose calculus for designing two-stage adaptive procedures. We describe the design components that specify a two-stage adaptive design, define their relationships, and demonstrate how changes in one design component effect changes in the other components. Our technique allows us to control many aspects of a two-stage adaptive clinical trial, including the type I and type II error rates and specification on the performance characteristics of the design. Stage I components, namely sample size, type I error rate, and type II error rate, are found to be the most influential. [ABSTRACT FROM AUTHOR]

This article considers the problem of estimating the dispersion parameter in a Gaussian model that is intermediate between a model where the mean parameter is fully known (fixed) and a model where the mean parameter is completely unknown. One of the goals is to understand the implications of the two-step process of first selecting a model among a finite number of submodels, then estimating a parameter of interest after the model selection, but using the same sample data. The estimators are classified into global, two-step, and weighted estimators. Whereas the global-type estimators ignore the model space structure, the two-step estimators explore the structure adaptively and can be related to pretest estimators, and the weighted estimators are motivated by the Bayesian approach. Their performances are compared theoretically and through simulations using their risk functions based on a scale-invariant quadratic loss function. It is shown that in the variance estimation problem, efficiency gains arise by exploiting the submodel structure through the use of two-step and weighted estimators, especially when the number of competing submodels is few, but that this advantage may deteriorate or be lost altogether for some two-step estimators as the number of submodels increases or the distance between them decreases. Furthermore, it is demonstrated that weighted estimators, arising from properly chosen priors, outperform two-step estimators when there are many competing submodels or when the submodels are close to each other, whereas two-step estimators are preferred when the submodels are highly distinguishable. The results have implications for model averaging and model selection issues. [ABSTRACT FROM AUTHOR]

In this article we consider identification and estimation of a censored nonparametric location scale-model. We first show that in the case where the location function is strictly less than the (fixed) censoring point for all values in the support of the explanatory variables, the location function is not identified anywhere. In contrast, when the location function is greater or equal to the censoring point with positive probability, the location function is identified on the entire support, including the region where the location function is below the censoring point. In the latter case we propose a simple estimation procedure based on combining conditional quantile estimators for various higher quantiles. The new estimator is shown to converge at the optimal nonparametric rate with a limiting normal distribution. A small-scale simulation study indicates that the proposed estimation procedure performs well in finite samples. We also present an empirical illustration on unemployment insurance duration using administrative-level data from New Jersey. [ABSTRACT FROM AUTHOR]

This article addresses the focused information criterion (FIC) in standard methodology. Aspects of the Claeskens-Hjort focused paradigm include: (1) known true model, (2) nesting and (3) mean squared error. In the known true model, the focused paradigm starts with a true model that is known up to a finite-dimensional parameter. In nesting, the focused criterion, like much current methodology, requires that all potential models be nested within the true model. Mean squared error is concerned with variable selection problems where the variables are measured with different costs and the total cost of estimating a variable is bounded. The ability of FIC to focus on specific parameterized issues comes as a mixed blessing: Having the ability to focus is clearly a general advantage, whereas being forced to focus could be annoying, particularly when one is routinely estimating points along the mean function. There are ways to approach variable selection in regression.

Robust covariance estimation commonly proceeds by downweighting outliers. In this article we measure the "outlyingness" of a data point by the standardized distance between the point and its Kth nearest neighbor. The appropriate weights for robust estimation are found by a model-based mixture modeling approach that follows from considering the data cloud as a realization of a high-dimensional point process. To correct a potential bias when there are no outliers, we introduce a boundary correction procedure that artificially adds in extra outlying points; the resulting methodology is called nearest-neighbor variance estimation (NNVE). The strength of NNVE is its robustness against a large proportion of noise points and against deviation from normality of the signal. A consistency result for the method is established. Under some reasonable assumptions, it is shown that the covariance estimate is bounded and that each point has only bounded influence on the final estimates. NNVE outperformed the popular minimum volume ellipsoid (MVE) estimator in simulation studies, with a big improvement when the proportion of outliers was very large (>50%). In our simulation study, when the proportion of outliers was ≥ 50%, the mean squared error of the NNVE estimator of variance was at least 100 times smaller than that of the MVE estimator. The proposed estimator also outperformed MVE in cases where the underlying data distribution was not normal. Good performance of NNVE in several real examples is demonstrated. A potential drawback of NNVE is that data points condensed in moderate-sized clusters would be classified as signal. Even though we do not support approaches discarding moderate-sized clusters as outliers without checking, this feature of NNVE could be problematic, particularly when only the main data cloud is of interest. A simple diagnostic tool built on existing model-based clustering procedure is proposed. This procedure allows us to check whether there is more than one separate data cloud in the data after cleaning. It also supplies the central locations of the separated moderate-sized clusters, which allows further investigation. Finally, because NNVE reduces the problem of finding the robustness weights to a one-dimensional problem, it may be useful in high-dimensional problems, such as those encountered in data mining. [ABSTRACT FROM AUTHOR]

Cluster analysis is the automated search for groups of related observations in a dataset. Most clustering done in practice is based largely on heuristic but intuitively reasonable procedures, and most clustering method available in commercial software are also in this type. However, there is little systematic guidance associated with these methods for solving important practical questions that arise in cluster analysis, such as how many cluster are there, which clustering method should be used, and how should outlines be handled. We review a general methodology for model-based clustering that provides a principal statistical approach to these issues. We also show that this can be useful for other problems in multivariate analysis, such as discriminant analysis and multivariate density estimation. We give examples from medical diagnosis, minefield detection, cluster recovery from noisy data, and spatial density estimation. Finally, we mention limitations of the methodology and discuss recent developments in model based clustering for non-Gaussian data, high-dimensional datasets, large datasets, and Bayesian estimation. [ABSTRACT FROM AUTHOR]

The problem of nuisance covariate model specification is considered in Cox regression where the maximum semiparametric likelihood method is used to handle the missing covariate. A component of the covariates is modeled nonparametrically in achieve robustness against covariate model misspecification and to reduce the number of possibly intractable integrations involved in the parametric modeling of the covariates. The statistical properties of the proposed method are examined. It is found that in some important situations, the maximum semiparametric likelihood can be applied without making any additional parametric model assumptions on covariates. The proposed method can yield a more efficient estimator than the nonparametric imputation methods and does not require specification of the missingness mechanism when compared with the inverse probability weighting method. A real data example is analyzed to demonstrate use of the proposed method. [ABSTRACT FROM AUTHOR]

The Cox proportional hazards model with a random effects has been proposed for the analysis of data which consist of a large number of small clusters of correlated failure time observations. The class of linear transformation models, provides many useful alternatives to the Cox model or analyzing univariate failure time data. In this article, we generalize these models by incorporating random effects, which generate the dependence among the failure time within the cluster to handle correlated data. Inference and prediction procedures for such random, effects models are proposed. They are relatively simple compared with the methods based on the nonparametric maximum liklihood estimators for the Cox frailty model in the literature. Our proposals are illustrated with a data set from a well-known eye study. Extensive numerical studies are conducted to various robustness properties of the new procedures. [ABSTRACT FROM AUTHOR]

We propose simple and structured procedure for decomposing a vector of time series into trend, cycle, seasonal and irregular components. Contrary to common practice, we do not assume these components to be orthogonal conditional on their past. However, the state-space representation employed ensures that their estimates converge to values with null variances and covariances. Null variances rue very important as they ensure chat the components do not change when the sample increases, This lack of "revisions" is the most important feature of our method, in comparison with most alternative procedures. On the other hand, null covariances provide a solid statistical foundation for the decomposition, as it ensures that a given component can be analyzed and interpreted independently of any other component(s). Other convenient properties of our method derive from the use of a state-space approach. First, defining the problem in state-space avoids dependence on particular model specifications, so the same procedure can he applied to a wide class of data representations, including ARIMA. VARMAX, univariate transfer functions, and structural time series models, Also, stale space methods deal easily with nonstandard situations, such as samples with missing values or constraints upon the structural components. Practical application of the procedure is illustrated with both simulated and real data. A MATLAB toolbox for lime series modeling and decomposition is available via the Internet. [ABSTRACT FROM AUTHOR]

By viewing quadrate and other second-order finite population functions as totals or means over a derived synthetic finite population, we show that the recently proposed model calibration and pseudoempirical liklihood method for effective use of auxiliary information from survey data can be readily extended to obtain efficient estimators of quadratic and other second-order finite population functions. In particular, estimation of a finite population variance, covariance, or variance of a linear estimator can be greatly improved when auxiliary information is available. The proposed methods are model assisted in that the resulting estimators are asymptotically design unbiased irrespective of the correctness of a working model but very efficient if the working model is nearly correct. They have a number of attractive features, which include applicability to a general sampling design, incorporation of information on possibly multivariate auxiliary variables and the ability to entertain linear or nonlinear working models, and they result in nonnegative estimates for certain strictly positive quantities such as variances. Several existing estimators are shown to be special cases of the proposal general methodology under a linear working model. [ABSTRACT FROM AUTHOR]

`Suppose that the finite population consists of N identifiable units, Associated with the ith unit are the study variable, Y1, and a vector of auxiliary variables, X1. The values X1, X2, …, XN are known for the entire population (i.e., complete) but y1 is known only if the ith unit is selected in the sample. One of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage. In this article, a unfied model-assisted framework has been attempted using a proposed model-calibration technique. The proposed model-calibration estimators can handle any linear or nonlinear working models and reduce to the conventional calibration estimators of Deville and Särndal and/or the generalized regression estimators in the linear model case. The pseudoempirical maximum likelihood estimator of Chen and Sitter, when used in this setting, gives an estimator that is asymptotically equivalent to the model-calibration estimator of but with positive weights. Some existing estimators using auxiliary information are reexamined under this framework. The estimation of the finite population distribution function, using complete auxiliary information, is also considered, and estimators based on a general model are presented. Results of a limited simulation study on the performance of the proposed estimators are reported. [ABSTRACT FROM AUTHOR]

Discovery and development a new drug can cost hundreds of millions of dollars, Pharmaceutical companies have used group testing methodology routinely as one of the efficient high throughput screening techniques to search for "lead" compounds among collections of hundreds of thousands of chemical compounds. The lead compounds can be modified to produce new and effective molecules, which eventually may lead to new drugs. This article develops models and estimation procedures to obtain quantitative information from data in such applications. It investigates groups testing procedures and studies can efficiency when the standard assumption adopted by Dorfman, that tested items are independently of one another, is violated. The investigation is focused on, but not limited to, the square array pooling method, and the methodologies developed are illustrated though simulations and a drug discovery dataset from Glaxo Wellcome Inc. [ABSTRACT FROM AUTHOR]