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This paper presents a novel data-driven bandwidth selector compatible with the small bandwidth asymptotics developed in Cattaneo, Crump, and Jansson (2009) for density-weighted average derivatives. The new bandwidth selector is of the plug-in variety, and is obtained based on a mean squared error expansion of the estimator of interest. An extensive Monte Carlo experiment shows a remarkable improvement in performance when the bandwidth-dependent robust inference procedures proposed by Cattaneo, Crump, and Jansson (2009) are coupled with this new data-driven bandwidth selector. The resulting robust data-driven confidence intervals compare favorably to the alternative procedures available in the literature. The online supplemental material to this paper contains further results from the simulation study. [ABSTRACT FROM AUTHOR]

The impact of dependence between individual test statistics is currently among the most discussed topics in the multiple testing of high-dimensional data literature, especially since Benjamini and Hochberg (1995) introduced the false discovery rate (FDR). Many papers have first focused on the impact of dependence on the control of the FDR. Some more recent works have investigated approaches that account for common information shared by all the variables to stabilize the distribution of the error rates. Similarly, we propose to model this sharing of information by a factor analysis structure for the conditional variance of the test statistics. It is shown that the variance of the number of false discoveries increases along with the fraction of common variance. Test statistics for general linear contrasts are deduced, taking advantage of the common factor structure to reduce the variance of the error rates. A conditional FDR estimate is proposed and the overall performance of multiple testing procedure is shown to be markedly improved, regarding the nondiscovery rate, with respect to classical procedures. The present methodology is also assessed by comparison with leading multiple testing methods. [ABSTRACT FROM AUTHOR]

In modern scientific research, data are often collected from multiple modalities. Since different modalities could provide complementary information, statistical prediction methods using multimodality data could deliver better prediction performance than using single modality data. However, one special challenge for using multimodality data is related to block-missing data. In practice, due to dropouts or the high cost of measures, the observations of a certain modality can be missing completely for some subjects. In this paper, we propose a new direct sparse regression procedure using covariance from multimodality data (DISCOM). Our proposed DISCOM method includes two steps to find the optimal linear prediction of a continuous response variable using block-missing multimodality predictors. In the first step, rather than deleting or imputing missing data, we make use of all available information to estimate the covariance matrix of the predictors and the cross-covariance vector between the predictors and the response variable. The proposed new estimate of the covariance matrix is a linear combination of the identity matrix, the estimates of the intra-modality covariance matrix and the cross-modality covariance matrix. Flexible estimates for both the sub-Gaussian and heavy-tailed cases are considered. In the second step, based on the estimated covariance matrix and the estimated cross-covariance vector, an extended Lasso-type estimator is used to deliver a sparse estimate of the coefficients in the optimal linear prediction. The number of samples that are effectively used by DISCOM is the minimum number of samples with available observations from two modalities, which can be much larger than the number of samples with complete observations from all modalities. The effectiveness of the proposed method is demonstrated by theoretical studies, simulated examples, and a real application from the Alzheimer's Disease Neuroimaging Initiative. The comparison between DISCOM and some existing methods also indicates the advantages of our proposed method. [ABSTRACT FROM AUTHOR]

Radiomics involves the study of tumor images to identify quantitative markers explaining cancer heterogeneity. The predominant approach is to extract hundreds to thousands of image features, including histogram features comprised of summaries of the marginal distribution of pixel intensities, which leads to multiple testing problems and can miss out on insights not contained in the selected features. In this paper, we present methods to model the entire marginal distribution of pixel intensities via the quantile function as functional data, regressed on a set of demographic, clinical, and genetic predictors to investigate their effects of imaging-based cancer heterogeneity. We call this approach quantile functional regression, regressing subject-specific marginal distributions across repeated measurements on a set of covariates, allowing us to assess which covariates are associated with the distribution in a global sense, as well as to identify distributional features characterizing these differences, including mean, variance, skewness, heavy-tailedness, and various upper and lower quantiles. To account for smoothness in the quantile functions, account for intrafunctional correlation, and gain statistical power, we introduce custom basis functions we call quantlets that are sparse, regularized, near-lossless, and empirically defined, adapting to the features of a given dataset and containing a Gaussian subspace so non-Gaussianness can be assessed. We fit this model using a Bayesian framework that uses nonlinear shrinkage of quantlet coefficients to regularize the functional regression coefficients and provides fully Bayesian inference after fitting a Markov chain Monte Carlo. We demonstrate the benefit of the basis space modeling through simulation studies, and apply the method to Magnetic resonance imaging (MRI)-based radiomic dataset from Glioblastoma Multiforme to relate imaging-based quantile functions to various demographic, clinical, and genetic predictors, finding specific differences in tumor pixel intensity distribution between males and females and between tumors with and without DDIT3 mutations. for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement. [ABSTRACT FROM AUTHOR]

Consider the model Y = X + ε with X = τ + Z , where τ is an unknown constant (the boundary of X), Z is a random variable defined on R + , ε is a symmetric error, and ε and Z are independent. Based on an iid sample of Y, we aim at identifying and estimating the boundary τ when the law of ε is unknown (apart from symmetry) and in particular its variance is unknown. We propose an estimation procedure based on a minimal distance approach and by making use of Laguerre polynomials. Asymptotic results as well as finite sample simulations are shown. The paper also proposes an extension to stochastic frontier analysis, where the model is conditional to observed variables. The model becomes Y = τ (w 1 , w 2) + Z + ε , where Y is a cost, w1 are the observed outputs and w2 represents the observed values of other conditioning variables, so Z is the cost inefficiency. Some simulations illustrate again how the approach works in finite samples, and the proposed procedure is illustrated with data coming from post offices in France. [ABSTRACT FROM AUTHOR]

Understanding and developing a correlation measure that can detect general dependencies is not only imperative to statistics and machine learning, but also crucial to general scientific discovery in the big data age. In this paper, we establish a new framework that generalizes distance correlation (Dcorr)—a correlation measure that was recently proposed and shown to be universally consistent for dependence testing against all joint distributions of finite moments—to the multiscale graph correlation (MGC). By using the characteristic functions and incorporating the nearest neighbor machinery, we formalize the population version of local distance correlations, define the optimal scale in a given dependency, and name the optimal local correlation as MGC. The new theoretical framework motivates a theoretically sound sample MGC and allows a number of desirable properties to be proved, including the universal consistency, convergence, and almost unbiasedness of the sample version. The advantages of MGC are illustrated via a comprehensive set of simulations with linear, nonlinear, univariate, multivariate, and noisy dependencies, where it loses almost no power in monotone dependencies while achieving better performance in general dependencies, compared to Dcorr and other popular methods. for this article are available online. [ABSTRACT FROM AUTHOR]

Social and medical scientists are often concerned that the external validity of experimental results may be compromised because of heterogeneous treatment effects. If a treatment has different effects on those who would choose to take it and those who would not, the average treatment effect estimated in a standard randomized controlled trial (RCT) may give a misleading picture of its impact outside of the study sample. Patient preference trials (PPTs), where participants' preferences over treatment options are incorporated in the study design, provide a possible solution. In this paper, we provide a systematic analysis of PPTs based on the potential outcomes framework of causal inference. We propose a general design for PPTs with multi-valued treatments, where participants state their preferred treatments and are then randomized into either a standard RCT or a self-selection condition. We derive nonparametric sharp bounds on the average causal effects among each choice-based subpopulation of participants under the proposed design. We also propose a sensitivity analysis for the violation of the key ignorability assumption sufficient for identifying the target causal quantity. The proposed design and methodology are illustrated with an original study of partisan news media and its behavioral impact. for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement. [ABSTRACT FROM AUTHOR]

This article highlights the historical events that took place within 50 years since the American Statistical Association was founded in 1839 and the Journal of the American Statistical Association (JASA) was first published in 1888. For the first years, JASA contained almost exclusively nonmathematical papers. Many were mere repositories of extensive data sets, including many compilations from census counts with interpretations of what these data purportedly revealed. Others were from investigations undertaken by sociologists, economists, political scientists and historians. One area that attracted theoretical attention dealt with the concepts of averages, variation and distributions. The second area that received theoretical attention during these years was correlation and related concepts.

It is of fundamental interest in statistics to test the significance of a set of covariates. For example, in genome-wide association studies, a joint null hypothesis of no genetic effect is tested for a set of multiple genetic variants. The minimum p-value method, higher criticism, and Berk–Jones tests are particularly effective when the covariates with nonzero effects are sparse. However, the correlations among covariates and the nonGaussian distribution of the response pose a great challenge toward the p-value calculation of the three tests. In practice, permutation is commonly used to obtain accurate p-values, but it is computationally very intensive, especially when we need to conduct a large amount of hypothesis testing. In this paper, we propose a Gaussian approximation method based on a Monte Carlo scheme, which is computationally more efficient than permutation while still achieving similar accuracy. We derive nonasymptotic approximation error bounds that could vanish in the limit even if the number of covariates is much larger than the sample size. Through real-genotype-based simulations and data analysis of a genome-wide association study of Crohn's disease, we compare the accuracy and computation cost of our proposed method, of permutation, and of the method based on asymptotic distribution. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

Graphical models have attracted increasing attention in recent years, especially in settings involving high-dimensional data. In particular, Gaussian graphical models are used to model the conditional dependence structure among multiple Gaussian random variables. As a result of its computational efficiency, the graphical lasso (glasso) has become one of the most popular approaches for fitting high-dimensional graphical models. In this paper, we extend the graphical models concept to model the conditional dependence structure among p random functions. In this setting, not only is p large, but each function is itself a high-dimensional object, posing an additional level of statistical and computational complexity. We develop an extension of the glasso criterion (fglasso), which estimates the functional graphical model by imposing a block sparsity constraint on the precision matrix, via a group lasso penalty. The fglasso criterion can be optimized using an efficient block coordinate descent algorithm. We establish the concentration inequalities of the estimates, which guarantee the desirable graph support recovery property, that is, with probability tending to one, the fglasso will correctly identify the true conditional dependence structure. Finally, we show that the fglasso significantly outperforms possible competing methods through both simulations and an analysis of a real-world electroencephalography dataset comparing alcoholic and nonalcoholic patients. [ABSTRACT FROM AUTHOR]

In this paper, we derive the asymptotic distribution of normalized residual empirical autocovariances and autocorrelations under weak assumptions on the noise. We propose new portmanteau statistics for vector autoregressive moving average models with uncorrelated but nonindependent innovations by using a self-normalization approach. We establish the asymptotic distribution of the proposed statistics. This asymptotic distribution is quite different from the usual chi-squared approximation used under the independent and identically distributed assumption on the noise, or the weighted sum of independent chi-squared random variables obtained under nonindependent innovations. A set of Monte Carlo experiments and an application to the daily returns of the CAC40 is presented. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

The paper is concerned with randomized experiments with one treatment. Two randomization schemes are considered: randomized pairs and unrestricted randomization. If effective at all, the treatment is supposed to affect the conditional distribution of the "experimental" variable Y given another variable X, called "predictor". The distribution of X is not affected by the treatment. Using the general theory published elsewhere, the paper deduces the locally asymptotically optimal test of the hypothesis that the treatment has no effect. Apart from the usual difficulties connected with asymptotic tests (how large must N be?), the theory is easily applicable in many "live" cases even though the conditional distribution of Y given X may contain nuisance parameters and be of unusual form. [ABSTRACT FROM AUTHOR]

This article studies the problem of modeling relationship between two spherical (or directional) random variables in a regression setup. Here the predictor and the response variables are constrained to be on a unit sphere and, due to this nonlinear condition, the standard Euclidean regression models do not apply. Several past papers have studied this problem, termed spherical regression, by modeling the response variable with a von Mises-Fisher (VMF) density with the mean given by a rotation of the predictor variable. The few papers that go beyond rigid rotations are limited to one- or two-dimensional spheres. This article extends the mean transformations to a larger group—the projective linear group of transformations—on unit spheres of arbitrary dimensions, while keeping the VMF density to model the noise. It develops a Newton–Raphson algorithm on the special linear group for estimating the MLE of regression parameter and establishes its asymptotic properties when the sample-size becomes large. Through a variety of experiments, using data taken from projective shape analysis, cloud tracking, etc., and some simulations, this article demonstrates improvements in the prediction and modeling performance of the proposed framework over previously used models. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

This article offers information on articles or manuscripts received by the "Journal of the American Statistical Association" in 1996. There have been 125 new submissions for the Applications and Case Studies section compared to 127 in 1997. There were 135 papers accepted and 452 papers were rejected for the Theory and Methods section.

We consider large-scale studies in which there are hundreds or thousands of correlated cases to investigate, each represented by its own normal variate, typically a z-value. A familiar example is provided by a microarray experiment comparing healthy with sick subjects' expression levels for thousands of genes. This paper concerns the accuracy of summary statistics for the collection of normal variates, such as their empirical cdf or a false discovery rate statistic. It seems like we must estimate an N by N correlation matrix, N the number of cases, but our main result shows that this is not necessary: good accuracy approximations can be based on the root mean square correlation over all N ⋅ ( N − 1)/2 pairs, a quantity often easily estimated. A second result shows that z-values closely follow normal distributions even under nonnull conditions, supporting application of the main theorem. Practical application of the theory is illustrated for a large leukemia microarray study. [ABSTRACT FROM AUTHOR]

The functional mobility of the elderly is a very important factor in aging research, and prognostic information is valuable in making clinical and health care policy decisions. We develop a predictive model for the functional status of the elderly based on data from the Second Longitudinal Study of Aging (LSOA II). The functional status is an ordinal response variable. The ordered probit model has been moderately successful in analyzing such data; however, its reliance on the normal distribution for its latent variable hinders its accuracy and potential. In this paper, we focus on the prediction of conditional quantiles of the functional status based on a more general transformation model. The proposed estimation procedure does not rely on any parametric specification of the conditional distribution functions, aiming to reduce model misspecification errors in the prediction. Cross-validation within the LSOA II data shows that our prediction intervals are more informative than those from the ordered probit model. Monte Carlo simulations also demonstrate the merits of our approach in the analysis of ordinal response variables. [ABSTRACT FROM AUTHOR]

In close elections, the losing side has an incentive to obtain evidence that the election result is incorrect. Sometimes this evidence comes in the form of court testimony from a sample of invalid voters, and this testimony is used to adjust vote totals (Belcher v. Mayor of Ann Arbor 1978; Borders v. King County 2005). However, while courts may be reluctant to make explicit findings about out-of-sample data (e.g., invalid voters that do not testify), when samples are used to adjust vote totals, the court is making such findings implicitly. In this paper, we show that the practice of adjusting vote totals on the basis of potentially unrepresentative samples can lead to incorrectly voided election results. More generally, we demonstrate that even when frame error and measurement error are minimal, random samples of post-vote vote-choice data can have limited power to detect incorrect election results without high response rates, precinct level polarization, or the acceptance of large Type I error rates. Therefore, in U.S. election disputes, even high-quality post-vote vote-choice data may be insufficient to resolve contested elections without the use of modeling assumptions (whether or not these assumptions are acknowledged). [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]

Missing data is a ubiquitous problem in medical and social sciences. It is well known that inferences based only on the complete data may not only lose efficiency, but may also lead to biased results if the data is not missing completely at random (MCAR). The inverse-probability weighting method proposed by Horvitz and Thompson (1952) is a popular alternative when the data is not MCAR. The Horvitz-Thompson method, however, is sensitive to the inverse weights and may suffer from loss of efficiency. In this paper, we propose a unified empirical likelihood approach to missing data problems and explore the use of empirical likelihood to effectively combine unbiased estimating equations when the number of estimating equations is greater than the number of unknown parameters. One important feature of this approach is the separation of the complete data unbiased estimating equations from the incomplete data unbiased estimating equations. The proposed method can achieve semiparametric efficiency if the probability of missingness is correctly specified. Simulation results show that the proposed method has better finite sample performance than its competitors. Supplemental materials for this paper, including proofs of the main theoretical results and the R code used for the NHANES example, are available online on the journal website. [ABSTRACT FROM AUTHOR]

Starting with the seminal paper of Haario, Saksman, and Tamminen (Haario, Saksman, and Tamminen 2001). a substantial amount of work has been done to validate adaptive Markov chain Monte Carlo algorithms. In this paper we focus on two practical aspects of adaptive Metropolis samplers. First, we draw attention to the deficient performance of standard adaptation when the target distribution is multimodal. We propose a parallel chain adaptation strategy that incorporates multiple Markov chains which are run in parallel. Second, we note that the current adaptive MCMC paradigm implicitly assumes that the adaptation is uniformly efficient on all regions of the state space. However, in many practical instances, different "optimal" kernels are needed in different regions of the state space. We propose here a regional adaptation algorithm in which we account for possible errors made in defining the adaptation regions. This corresponds to the more realistic case in which one does not know exactly the optimal regions for adaptation. The methods focus on the random walk Metropolis sampling algorithm but their scope is much wider. We provide theoretical justification for the two adaptive approaches using the existent theory build for adaptive Markov chain Monte Carlo. We illustrate the performance of the methods using simulations and analyze a mixture model for real data using an algorithm that combines the two approaches. [ABSTRACT FROM AUTHOR]

The article focuses on the intuitive derivation provided by the author to resolve the problem on fast convergence rates in the article "Nonparametric Prediction in Measurement Error Models," by R. J. Caroll and colleagues. It discloses the replacement of unbiased quantity in Equation 2.1 to provide efficiency in exploiting the potential heteroscedasticity in the data. Furthermore, it reveals the pointwise convergence rate estimator and the application of regression calibration.

Professor Efron has presented us with a thought-provoking paper on the relationship between prediction, estimation, and attribution in the modern era of data science. While we appreciate many of his arguments, we see more of a continuum between the old and new methodology, and the opportunity for both to improve through their synergy. [ABSTRACT FROM AUTHOR]

This article comments on the article by Barnard, Frangakis, Hill, and Rubin discussing the results of the New York City school choice experiments based on one-year achievement outcomes. The New York City school voucher experiment provides some of the strongest evidence on the effect of private school vouchers on student test achievement yet available. Barnard et al. provide a useful reevaluation of the experiment, and some of the authors were integrally involved in the design of the experiment. The authors will leave it to other discussants to comment on the Bayesian methodological advances in their paper, and instead comment on the substantive lessons that can be learned from the experiment, and the practical lessons that emerge from the novel design of the experiment. The authors have the advantage of having access to more complete data than Barnard et al. used in preparing their paper. This includes more complete baseline test information, data on multi-child families as well as single-child families, and three years of follow-up test data instead of just one year of follow-up data. In this comment, the authors use the more comprehensive sample because results for this sample are more informative, but we highlight where differences arise from using the sample analyzed by Barnard et al. Three themes emerge from our analysis. First, simplicity and transparency are under appreciated virtues in statistical analysis. Second, it is desirable to use the most recent, comprehensive data, for the widest sample possible. Third, there is no substitute for probing the definitions and concepts that underlie the data.

Presents the author's views on the design and analysis of the clinical trial for Acquired Immune Deficiency Syndrome (AIDS). Information about the complications of trial design for this unique disease; View that the level of discussion in the paper is necessarily non-technical and lacking detail; Discussion on surrogate endpoints in AIDS; View that the authors should give more space to the time urgency of the problems of AIDS.

The article offers a discussion on a novel estimation of the average causal effects of the treatment strategies in the presence of time dependent confounding by indication. Topics discussed include penalized spline of propensity methods in handling missing data to causal inference incorporating a temporal element into consideration; and concludes that different approaches such as modeling and algorithms can be adopted to incorporate the propensity score.

A century ago, postage stamps were printed on a deliberate mixture of different paper types, each having its own thickness characteristics due to poor quality control in paper manufacture. It was not unusual for different types of paper to be used for a single stamp issue, because ordinary white wove paper was often not readily available in quantities necessary for production of a new stamp issue. Unfortunately, the different paper types used were not always well documented. Each paper type was purchased by the ream, which was required to consist of a specific number of sheets and had to weigh a certain amount. To cut costs, manufacturers often satisfied both requirements by mixing a few "thick" sheets of paper into an otherwise underweight ream. Although the importance of paper thickness in the philatelic literature is reflected by a higher market value for stamps printed on the thicker and more scarce paper, stamp catalogs have been notoriously vague about characterizing paper thickness, relying instead on classifying stamps by whether they were printed on "thin," "regular," or "thick" paper. In this article, the term philatelic mixture is introduced to describe any situation in which a particular stamp issue is known to have been printed on a mixture of paper types with possible differences in paper thickness. In statistical terms, this is a mixture-of-distributions problem, in which identification of the mixture components (different paper types) is achieved using measurements on stamp thickness, and where information regarding the number of such components is vague, at best. The focus of this article is on parametric and nonparametric perspectives of the mixture problem and its special application to identifying the components of philatelic mixtures. The parametric approach tries to fit a finite mixture of component densities of a given type, usually normal, where... [ABSTRACT FROM AUTHOR]

A data set consisting of 143 rankings of 10 occupations from a survey of Goldberg has been analyzed in a number of recent papers. The purpose of this paper is to use so-called "nested orthogonal contrasts" of the occupations to gain further insight into the data. A contrast is a comparison of subsets of the occupations based on their relative ranks, contrasts are orthogonal if the comparisons they represent are not confounded. Various models based on sets of orthogonal contrasts—including contingency table models, models analogous to those of Fligner and Verducci, and latent class models—are applied to the data. It is found that there are three main groups of occupations based on overall prestige, and within each group are distinctions between managerial and technical occupations. [ABSTRACT FROM AUTHOR]

This paper presents a reparameterization of the conventional log-linear regression model. This reparameterization is shown to be more reasonable than the conventional specification. The stochastic assumptions of this reparameterized model are derived from the expected value properties of the dependent variable. Comparison with the conventional method of fitting log-linear models shows the regression intercept and the variance of the regression intercept to be different. A minimum variance unbiased estimate and another consistent estimate of the intercept are derived. [ABSTRACT FROM AUTHOR]

This paper gives analytic expressions for the distribution function of t", a doubly noncentral t-distribution, with nu degrees of freedom and noncentrality parameters delta and lambda, in series of Incomplete Beta and Hypergeometric (Gauss and Confluent) functions. Numerical values of Pr(t" ≤ t|v, δ, λ) for v = 2 (1) 20, λ = 0 (2) 8, |δ| = 0 (1) 5, t=0 and 1 are given in Table I. [ABSTRACT FROM AUTHOR]

The author [1], [2] has given an algorithm for finding that stratified allocation which minimizes the posterior variance of the overall population mean subject to a budget constraint under a model in which a normal prior distribution and independent normal sampling distributions were assumed. The budget constraint assumed a variable per unit cost of observation. In the present paper these results are extended to cover the case where there are fixed costs, as well as variable costs, associated with sampling in the ith stratum. The resulting algorithm is noted to be applicable in finding the optimal allocation of sampling effort (with fixed and variable sampling costs) under a variety of distributional assumptions. An interpretation is also given to two and higher stage design questions when there is differential prior information regarding the first stage units. [ABSTRACT FROM AUTHOR]

This paper compares the Pearson Chi-Square and Kolmogorov goodness-of-fit tests with respect to validity under the following conditions: (1) the N independent observations are tabulated and arranged into k mutually exclusive groups that are equally probable under the hypothesis to be tested; and (2) both N and k are "small"; i.e., not greater than 50. A random sampling experiment was performed, and the results show that in general for the conditions considered, the Pearson test is more valid than the Kolmogorov test. [ABSTRACT FROM AUTHOR]

The author comments on the research conducted by Ruth Heller, Tony Cai, Peter Westfall and Armin Schwartzman on the accuracy of summary statistics in large-scale testing in the U.S. The author believes that Cai and Heller wrote authoritatively on the topics. He believes that there are missing discussion on their research regarding the use of ordinary nonparametric bootstrapping to asnwer simple accuracy questions.

The use of high-power industrial equipment, such as large-scale mixing equipment or a hydrocyclone for separation of particles in liquid suspension, demands careful monitoring to ensure correct operation. The fundamental task of state-estimation for the liquid suspension can be posed as a time-evolving inverse problem and solved with Bayesian statistical methods. In this article, we extend Bayesian methods to incorporate statistical models for the error that is incurred in the numerical solution of the physical governing equations. This enables full uncertainty quantification within a principled computation-precision trade-off, in contrast to the over-confident inferences that are obtained when all sources of numerical error are ignored. The method is cast within a sequential Monte Carlo framework and an optimized implementation is provided in Python. [ABSTRACT FROM AUTHOR]

Examines a general class of piecewise stationary processes that allows changes in spectral characteristics of nonstationary time series. Use of process to model natural phenomena; Proposal for an adaptive segmentation method to estimate time-dependent spectrum; Applications of the method to speech signals and earthquake data.

We consider the problem of finding optimal nonsequential designs for a large class of regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function. Since the design weights can be found easily by existing methods once the support is known, we concentrate on determining the support of the optimal design. The proposed method treats D-, E-, A-, and Φ p -optimal designs in a unified manner, and generates a polynomial whose zeros are the support points of the optimal approximate design, generalizing a number of previously known results of the same flavor. The method is based on a mathematical optimization model that can incorporate various criteria of optimality and can be solved efficiently by well-established numerical optimization methods. In contrast to optimization-based methods previously proposed for the solution of similar design problems, our method also has theoretical guarantee of its algorithmic efficiency; in concordance with the theory, the actual running times of all numerical examples considered in the paper are negligible. The numerical stability of the method is demonstrated in an example involving high-degree polynomials. As a corollary, an upper bound on the size of the support set of the minimally supported optimal designs is also found. [ABSTRACT FROM AUTHOR]

With the recent availability of high-frequency financial data the long-range dependence of volatility regained researchers' interest and has led to the consideration of long-memory models for volatility. The long-range diagnosis of volatility, however, is usually stated for long sample periods, while for small sample sizes, such as one year, the volatility dynamics appears to be better described by short-memory processes. The ensemble of these seemingly contradictory phenomena point towards short-memory models of volatility with nonstationarities, such as structural breaks or regime switches, that spuriously generate a long memory pattern. In this paper we adopt this view on the dependence structure of volatility and propose a localized procedure for modeling realized volatility. That is at each point in time we determine a past interval over which volatility is approximated by a local linear process. A simulation study shows that long memory processes as well as short memory processes with structural breaks can be well approximated by this local approach. Furthermore, using S&P500 data we find that our local modeling approach outperforms long-memory type models and models with structural breaks in terms of predictability. [ABSTRACT FROM AUTHOR]

Copulas have proven to be very successful tools for the flexible modeling of cross-sectional dependence. In this paper we express the dependence structure of continuous-valued time series data using a sequence of bivariate copulas. This corresponds to a type of decomposition recently called a 'vine' in the graphical models literature, where each copula is entitled a 'pair-copula.' We propose a Bayesian approach for the estimation of this dependence structure for longitudinal data. Bayesian selection ideas are used to identify any independence pair-copulas, with the end result being a parsimonious representation of a time-inhomogeneous Markov process of varying order. Estimates are Bayesian model averages over the distribution of the lag structure of the Markov process. Using a simulation study we show that the selection approach is reliable and can improve the estimates of both conditional and unconditional pairwise dependencies substantially. We also show that a vine with selection outperforms a Gaussian copula with a flexible correlation matrix. The advantage of the pair-copula formulation is further demonstrated using a longitudinal model of intraday electricity load. Using Gaussian, Gumbel, and Clayton pair-copulas we identify parsimonious decompositions of intraday serial dependence, which improve the accuracy of intraday load forecasts. We also propose a new diagnostic for measuring the goodness of fit of high-dimensional multivariate copulas. Overall, the pair-copula model is very general and the Bayesian method generalizes many previous approaches for the analysis of longitudinal data. Supplemental materials for the article are also available online. [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 situations where individuals are screened for an infectious disease or other binary characteristic and where resources for testing are limited, group testing can offer substantial benefits. Group testing, where subjects are tested in groups (pools) initially, has been successfully applied to problems in blood bank screening, public health, drug discovery, genetics, and many other areas. In these applications, often the goal is to identify each individual as positive or negative using initial group tests and subsequent retests of individuals within positive groups. Many group testing identification procedures have been proposed; however, the vast majority of them fail to incorporate heterogeneity among the individuals being screened. In this paper, we present a new approach to identify positive individuals when covariate information is available on each. This covariate information is used to structure how retesting is implemented within positive groups; therefore, we call this new approach 'informative retesting.' We derive closed-form expressions and implementation algorithms for the probability mass functions for the number of tests needed to decode positive groups. These informative retesting procedures are illustrated through a number of examples and are applied to chlamydia and gonorrhea testing in Nebraska for the Infertility Prevention Project. Overall, our work shows compelling evidence that informative retesting can dramatically decrease the number of tests while providing accuracy similar to established noninformative retesting procedures. This article has supplementary material online. [ABSTRACT FROM AUTHOR]

Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing summary statistics s obs from the data and simulating summary statistics for different values of the parameter Θ. The posterior distribution is then approximated by an estimator of the conditional density g( Θ| s obs). In this paper, we derive the asymptotic bias and variance of the standard estimators of the posterior distribution which are based on rejection sampling and linear adjustment. Additionally, we introduce an original estimator of the posterior distribution based on quadratic adjustment and we show that its bias contains a fewer number of terms than the estimator with linear adjustment. Although we find that the estimators with adjustment are not universally superior to the estimator based on rejection sampling, we find that they can achieve better performance when there is a nearly homoscedastic relationship between the summary statistics and the parameter of interest. To make this relationship as homoscedastic as possible, we propose to use transformations of the summary statistics. In different examples borrowed from the population genetics and epidemiological literature, we show the potential of the methods with adjustment and of the transformations of the summary statistics. Supplemental materials containing the details of the proofs are available online. [ABSTRACT FROM AUTHOR]

This paper proposes a methodology for combining satellite images with advection-diffusion models for interpolation and prediction of environmental processes. We propose a dynamic state-space model and an ensemble Kalman filter and smoothing algorithm for on-line and retrospective state estimation. Our approach addresses the high dimensionality, measurement bias, and nonlinearities inherent in satellite data. We apply the method to a sequence of SeaWiFS satellite images in Lake Michigan from March 1998, when a large sediment plume was observed in the images following a major storm event. Using our approach, we combine the images with a sediment transport model to produce maps of sediment concentrations and uncertainties over space and time. We show that our approach improves out-of-sample RMSE by 20%-30% relative to standard approaches. This article has supplementary material online. [ABSTRACT FROM AUTHOR]

Multiplicative regression model or accelerated failure time model, which becomes linear regression model after logarithmic transformation, is useful in analyzing data with positive responses, such as stock prices or life times, that are particularly common in economic/financial or biomedical studies. Least squares or least absolute deviation are among the most widely used criterions in statistical estimation for linear regression model. However, in many practical applications, especially in treating, for example, stock price data, the size of relative error, rather than that of error itself, is the central concern of the practitioners. This paper offers an alternative to the traditional estimation methods by considering minimizing the least absolute relative errors for multiplicative regression models. We prove consistency and asymptotic normality and provide an inference approach via random weighting. We also specify the error distribution, with which the proposed least absolute relative errors estimation is efficient. Supportive evidence is shown in simulation studies. Application is illustrated in an analysis of stock returns in Hong Kong Stock Exchange. [ABSTRACT FROM AUTHOR]

The paper proposes two inferential tests for error correlation in the functional linear model, which complement the available graphical goodness-of-fit checks. To construct them, finite dimensional residuals are computed in two different ways, and then their autocorrelations are suitably defined. From these autocorrelation matrices, two quadratic forms are constructed whose limiting distribution are chi-squared with known numbers of degrees of freedom (different for the two forms). The asymptotic approximations are suitable for moderate sample sizes. The test statistics can be relatively easily computed using the package , or similar MATLAB software. Application of the tests is illustrated on magnetometer and financial data. The asymptotic theory emphasizes the differences between the standard vector linear regression and the functional linear regression. To understand the behavior of the residuals obtained from the functional linear model, the interplay of three types of approximation errors must be considered, whose sources are: projection on a finite dimensional subspace, estimation of the optimal subspace, and estimation of the regression kernel. [ABSTRACT FROM AUTHOR]

A longstanding problem in clinical research is distinguishing drug-treated subjects that respond due to specific effects of the drug from those that respond to nonspecific (or placebo) effects of the treatment. Linear mixed effect models are commonly used to model longitudinal clinical trial data. In this paper we present a solution to the problem of identifying placebo responders using an optimal partitioning methodology for linear mixed effects models. Since individual outcomes in a longitudinal study correspond to curves, the optimal partitioning methodology produces a set of prototypical outcome profiles. The optimal partitioning methodology can accommodate both continuous and discrete covariates. The proposed partitioning strategy is compared and contrasted with the growth mixture modeling approach. The methodology is applied to a two-phase depression clinical trial where subjects in a first phase were treated openly for 12 weeks with fluoxetine followed by a double blind discontinuation phase where responders to treatment in the first phase were randomized to either stay on fluoxetine or switched to a placebo. The optimal partitioning methodology is applied to the first phase to identify prototypical outcome profiles. Using time to relapse in the second phase of the study, a survival analysis is performed on the partitioned data. The optimal partitioning results identify prototypical profiles that distinguish whether subjects relapse depending on whether or not they stay on the drug or are randomized to a placebo. [ABSTRACT FROM AUTHOR]

In longitudinal clinical trials, when outcome variables at later time points are only defined for patients who survive to those times, the evaluation of the causal effect of treatment is complicated. In this paper, we describe an approach that can be used to obtain the causal effect of three treatment arms with ordinal outcomes in the presence of death using a principal stratification approach. We introduce a set of flexible assumptions to identify the causal effect and implement a sensitivity analysis for nonidentifiable assumptions which we parameterize parsimoniously. Methods are illustrated on quality of life data from a recent colorectal cancer clinical trial. This article has supplementary material online. [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]

Multidimensional scaling (MDS) comprises a family of geometric models for the multidimensional representation of data and a corresponding set of methods for fitting such models to actual data. In this paper, we develop a new Bayesian vector MDS model to analyze ordered successive categories preference/dominance data commonly collected in many social science and business studies. A joint spatial representation of the row and column elements of the input data matrix is provided in a reduced dimensionality such that the geometric relationship of the row and column elements renders insight into the utility structure underlying the data. Unlike classical deterministic MDS procedures, the Bayesian method includes a probability based criterion to determine the number of dimensions of the derived joint space map and provides posterior interval as well as point estimates for parameters of interest. Also, our procedure models the raw integer successive categories data which ameliorates the need of any data preprocessing as required for many metric MDS procedures. Furthermore, the proposed Bayesian procedure allows external information in the form of an intractable posterior distribution derived from a related dataset to be incorporated as a prior in deriving the spatial representation of the preference data. An actual commercial application dealing with consumers’ intentions to buy new luxury sport utility vehicles are presented to illustrate the proposed methodology. Favorable comparisons are made with more traditional MDS approaches. [ABSTRACT FROM AUTHOR]

The dynamic hierarchical Dirichlet process (dHDP) is developed to model complex sequential data, with a focus on audio signals from music. The music is represented in terms of a sequence of discrete observations, and the sequence is modeled using a hidden Markov model (HMM) with time-evolving parameters. The dHDP imposes the belief that observations that are temporally proximate are more likely to be drawn from HMMs with similar parameters, while also allowing for “innovation” associated with abrupt changes in the music texture. The sharing mechanisms of the time-evolving model are derived, and for inference a relatively simple Markov chain Monte Carlo sampler is developed. Segmentation of a given musical piece is constituted via the model inference. Detailed examples are presented on several pieces, with comparisons to other models. The dHDP results are also compared with a conventional music-theoretic analysis. All the supplemental materials used by this paper are available online. [ABSTRACT FROM AUTHOR]

Mixture models, or convex combinations of a countable number of probability distributions, offer an elegant framework for inference when the population of interest can be subdivided into latent clusters having random characteristics that are heterogeneous between, but homogeneous within, the clusters. Traditionally, the different kinds of mixture models have been motivated and analyzed from very different perspectives, and their common characteristics have not been fully appreciated. The inferential techniques developed for these models usually necessitate heavy computational burdens that make them difficult, if not impossible, to apply to the massive data sets increasingly encountered in real world studies. This paper introduces a flexible class of models called generalized Pólya urn (GPU) processes. Many common mixture models, including finite mixtures, hidden Markov models, and Dirichlet processes, are obtained as special cases of GPU processes. Other important special cases include finite-dimensional Dirichlet priors, infinite hidden Markov models, analysis of densities models, nested Chinese restaurant processes, hierarchical DP models, nonparametric density models, spatial Dirichlet processes, weighted mixtures of DP priors, and nested Dirichlet processes. An investigation of the theoretical properties of GPU processes offers new insight into asymptotics that form the basis of cost-effective Markov chain Monte Carlo (MCMC) strategies for large datasets. These MCMC techniques have the advantage of providing inferences from the posterior of interest, rather than an approximation, and are applicable to different mixture models. The versatility and impressive gains of the methodology are demonstrated by simulation studies and by a semiparametric Bayesian analysis of high-resolution comparative genomic hybridization data on lung cancer. The appendixes are available online as supplemental material. [ABSTRACT FROM AUTHOR]

While Distance Weighted Discrimination (DWD) is an appealing approach to classification in high dimensions, it was designed for balanced datasets. In the case of unequal costs, biased sampling, or unbalanced data, there are major improvements available, using appropriately weighted versions of DWD (wDWD). A major contribution of this paper is the development of optimal weighting schemes for various nonstandard classification problems. In addition, we discuss several alternative criteria and propose an adaptive weighting scheme (awDWD) and demonstrate its advantages over nonadaptive weighting schemes under some situations. The second major contribution is a theoretical study of weighted DWD. Both high-dimensional low sample-size asymptotics and Fisher consistency of DWD are studied. The performance of weighted DWD is evaluated using simulated examples and two real data examples. The theoretical results are also confirmed by simulations. [ABSTRACT FROM AUTHOR]