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Given a population of N units, it is required to draw a sample of n distinct units in such a way that the probability for the ith unit to be in the sample is proportional to its 'size' x. From the alternative methods of achieving this we consider here only the so-called systematic method which, to the best of our knowledge, was first developed by W. G. Madow (1949): The units in the population are listed in a 'particular' order, their x, accumulated and a systematic selection of n elements from a 'random start' is then made on the accumulation. In a more recent paper (H. O. Hartley and J. N. K. Rao (1962) ) an asymptotic estimation theory (for large N) associated with this procedure was developed for the case when the order of the listed units is random. In this paper we draw attention to certain properties of Madow's estimator: We utilize the fact that with systematic sampling the total number of different samples is N (rather than ([This eq. cannot be change in char.]) as with completely random sampling). This simplification in the definition of the variance of the estimator in repeated sampling enables us to identify the exact variance of Madow's estimator with a 'between sample mean square' in a special analysis of variance (see section 4) and compare it with the variance of the pps estimator in sampling with replacement as well as in other sampling procedures. We also develop two approximate methods of variance estimation (see section 5). We pay particular attention to the case when the units are listed in the order of their size. With this particular arrangement our method can be described as 'systematic with random start' and the gain in precision that we accomplish has of course, analogues in systematic sampling with equal probabilities employing ratio estimators in which there is a relation between the ratio ri =yi/Xi and xi Compared with other methods the present procedure combines the advantage of ease of systematic sample selection with the availability of exact variance formulas for any n and N. Moreover, it usually leads to a more efficient estimate. Its shortcoming resides in the fact that the estimation of the variance is based on certain assumptions. [ABSTRACT FROM AUTHOR]

In educational and psychological applications as well as in other applications, it may be necessary to make certain comparisons of two regression lines when the variances are unequal. Such problems arise, for example, in studies comparing two alternative curriculums or two different teaching methods. By generalizing an idea which Scheffe used to obtain a test for the Behrens-Fisher problem, this paper develops some tests for comparing two regression lines when the two sets of error terms are normally distributed but with two different variances. Scheffe's test itself is a randomized test, but in this paper we present both randomized and non-randomized tests. Both simple and multiple regression are considered, but the simple regression tests are computationally easier than the multiple regression tests. The basic test statistic which is used is the ordinary t-statistic. Essentially two types of problems are dealt with: (A) determining whether the two regression lines are identical when they are known to be parallel; and (B) determining whether the two regression lines are parallel. Confidence bounds as well as tests of hypotheses are available. For Problem A, a minimax estimator of the distance between the two lines is obtained. In addition to the Scheffe-type tests, we also consider some tests based on an approach of Welch and Hajek. A numerical example is presented. [ABSTRACT FROM AUTHOR]

The article presents information about Samuel S. Wilks, a great contributor to statistics. Wilks' behavior toward applications was peculiarly split, he encouraged his students to work on applications, not always an easy thing to do in a strongly theoretical mathematics department; he often told students about applications that he regarded as "neat" or "cute" or "clever"; the statistical colloquium he guided often had speakers on practical applications of mathematical statistics; he himself wrote some practical papers in statistics, but in the classroom he rarely discussed applications. Repeatedly, however, practical problems explicitly influenced both his own publications and those of his students and Wilks often used applications as motivation for the discussion of distribution theory, usually going well beyond the needs of the original problem. The papers to be discussed exhibit incompletely and fragmentarily a major influence on the work of the man and his students. Wilks watched the development of the statistical theory of order statistics closely. Indeed he wrote a masterful summary of the literature. The general area involves the study of the statistical properties of ordered measurements.

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]

Various methods based on Student t variates have been suggested and used for obtaining simultaneous confidence intervals for several means, or for several contrasts among means. Determination of an overall confidence level for such intervals involves evaluating the probability mass of a multivariate t distribution over a hypercube centered at the origin, with sides paralleling the coordinate planes, or obtaining bounds for this probability mass. Since such distributions involve many nuisance parameters, an impossible number of tables would be necessary in order to make exact confidence intervals. In the virtual absence of tables, approximations and bounds become important. In this paper, an attempt has been made to investigate the adequacy of certain suggested approximations [2], [5], [8] by computing the exact distributions for some particular cases. These exact distributions have been compared with approximations. This paper is concerned with two-sided confidence intervals, rather than one-sided intervals. [ABSTRACT FROM AUTHOR]

In a previous paper [12], an attempt was made to show how spectral techniques could be used to compare the effects of two seasonal adjustment procedures on the series to which they were applied. The two procedures compared were: (a) the technique currently used by the Bureau of Labor Statistics for seasonally adjusting employment, unemployment, and labor force monthly statistics, and (b) the so-called "residual" method, proposed by Brittain [2], Samuelson [16], and others. Spectra of the original and the seasonally adjusted series and the cross spectrum of the two were used to aid in the assessment of whether either procedure removed more than could be considered seasonal, introduced spurious regularities, and/or distorted temporal relationships. It was concluded that both techniques removed more than seasonal effects from, and produced some temporal distortion in, the series to which they were applied. Neither method appeared to be superior to the other. It is the purpose of this paper to carry the previous analysis one step further and to compare the BLS procedure with a modified version of the regression method of seasonal adjustment suggested by Cowden [3] and Mendershausen [11], and recently revived by Harman [9, 10] in an exceptionally sophisticated form. In addition to Hannan's work along the lines suggested, Nettheim [13] and Rosenblatt [15] have made studies. Rosenblatt [15] has carried out analyses similar to those reported here. [ABSTRACT FROM AUTHOR]

This paper deals with the asymptotic relative efficiency (A.R.E.) and the asymptotic power of certain tests. These tests are distribution-free goodness-of-fit tests based on the empirical distribution function. They are the one and two sided Kolmogorov-Smirnov tests and a new one based on the absolute values of the order statistics. The method of obtaining the A.R.E. is due to Quade [5] and is outlined in Section 1. In this paper we are concerned with the case of scalar alternatives. The asymptotic power for the Kolmogorov-Smirnov tests is obtained in Section 2. Section 3 deals with a new test which allows a more facile use of a one-sided statistic while utilizing the same information normally included in a two-sided statistic. In Section 4, three examples are considered to illustrate the superiority of this new test. [ABSTRACT FROM AUTHOR]

In this article, the author will talk about researcher R.A. Fisher's contributions to statistics. It is well-known that his work in genetics was of comparable status. It is largely represented by his book "The Genetical Theory of Natural Selection," though in his subsequent work his further association with ecological and experimental studies in evolutionary genetics, and his share in the development of studies in the human blood groups, might especially be recalled. Fisher's contributions to statistics began with a paper in 1912 advocating the method of maximum likelihood for fitting frequency curves, although the first paper of substance was his 1915 paper in the journal "Biometrika," on the sampling distribution of the correlation coefficient. Fisher tried to pose problems of analysis as the reduction and simplification of statistical data. He put forward his well-known concept of amount of information in estimation theory, such that information might be lost, but never gained, by analysis. His concept has been of great practical value, especially in large sample theory.

The principal part of this paper is devoted to the study of the distribution and density functions of the ratio of two normal random variables. It gives several representations of the distribution function in terms of the vivariate normal distribution and Nicholson's V function, both of which have been extensively studied, and for which tables and computational procedures are readily available. One of these representations leads to an easy derivation of the density function in terms of the Cauchy density and the normal density and integral. A number of graphs of the possible shapes of the density are given, together with an indication of when the density is unimodal or bimodal. The last part of the paper discusses the distribution of the ratio (u[sub 1] + ... + u[sub n])/(v[sub I] + ... + v[sub m]) where the u's and v's are independent, uniform variables. The exact distribution for all n and m is given, and some approximations discussed. [ABSTRACT FROM AUTHOR]

The use of simulation, as a technique for attacking difficult problems, has increased greatly with the availability of the digital computer. This is illustrated by the large number of references in Shubik's (1960) bibliography[sup 2] and in the large number of studies published since then. Simulation is essentially an extension of a technique known as empirical sampling, or distribution sampling, which has been used in the field of statistics for many years. The limitations of the technique, which are well known to statisticians, are apparently not as well known, or at least not as well recognized, by those using simulation today. The first part of this paper contains an historical survey of distribution sampling as used by statisticians. The material was originally prepared in 1953 and is reproduced here in slightly revised form to bring this history to the attention of present day simulators in order that the lessons that can be learned from this part can more readily be incorporated in the development of methodology today. The second part of this paper discusses the relevance of empirical sampling to the present day state of the art of simulation. The technique of generating random members, developed for empirical sampling can be applied directly to simulation. However in other aspects simulation is more difficult than empirical sampling and here the theory of distribution sampling does not have much to offer. The difficulties are due to lack of independence among time series, non-stationarity of the time series, and the large number of parameters. [ABSTRACT FROM AUTHOR]

The article focuses on the study regarding the boundary of smoothing parameter space in statistical analysis. It mentions several papers by different authors which featured different approaches and methods to determine smoothing parameters on the edge of the feasible parameter space. It also describes the proposed fixes of the researchers that offer substantial improvement to the phase transition to smooth estimates to nonzero smoothing penalty.

Presents the authors' comments on the paper "Semilinear High-Dimensional Model for Normalization of Microarray Data: A Theoretical Analysis and Partial Consistency," by Jianqing Fan, Heng Peng, and Tao Huang, published in the September 2005 issue of the "Journal of the American Statistical Association." Congratulations to the authors for their interesting, innovative, and important contribution on microarray normalization; Analysis of the main contributions made by the authors; Suggestions for some possible extensions to the results of the authors; Views on the goal of significance analysis; Appreciation of the paper for its computational simplicity.

Presents the author's comments on the paper "Semilinear High-Dimensional Model for Normalization of Microarray Data: A Theoretical Analysis and Partial Consistency," by Jianqing Fan, Heng Peng and Tao Huang, published in the September 2005 issue of the "Journal of the American Statistical Association." Appreciation of the authors for their significant contribution in enlarging the bag of statistical tools available for normalization; Opinion on the normalization strategy described; Importance of the iterative procedure suggested; Views on the focus of the paper from a methodological standpoint; Contexts in which the methodology described may be applicable.

This article comments on a paper by Nozer D. Singpurwalla and Jane M. Booker which aimed to develop a line of argument that demonstrates that probability theory has a sufficiently rich structure for incorporating fuzzy sets within its framework. Google reports about 670,000 websites that connect with the phrase fuzzy logic. From a mathematical perspective, the concept of a fuzzy set is somewhat disconcerting, because a fuzzy set is generally not a set, but rather a variable. A crucial issue, which was debated already in the earliest days of fuzzy logic, concerns whether or not membership values are just probabilities in disguise. Certainly, the original motivating examples deal primarily with formalizing variables that correspond to natural language concepts that are in everyday use. The paper's section 4 introduces Lofti Zadeh's rejection of the law of the excluded middle, with reference to differentiating between membership values and probabilities. The commenter's reading of the paper's section 4, and of formula (1) in particular, suggests that Zadeh in 1968 might well have approved a solution along the lines of the preceding paragraph, except that he would have used the posterior expectation of m(x) as a summary of the posterior distribution.

This article comments on a paper by Nozer D. Singpurwalla and Jane M. Booker which aimed to develop a line of argument that probability theory has a sufficiently rich structure tor incorporating fuzzy sets within its framework. According to the commenter, the paper provides a real advance in the understanding of fuzzy sets, by providing a sensible connection between membership functions and likelihood, and thereby probability. He says the paper's modification of the basic question is answered most convincingly. However, the answer raises an apparent conflict between the two calculi of fuzzy logic and probability. What is now needed is a second article to resolve this conflict. The commenter's conjecture is that the resolution will show that the rules of fuzzy logic are untenable. According to him, his principal reason behind the conjecture is that the rules of the probability calculus follow from simple, obvious assumptions, whereas those of the fuzzy calculus have been arbitrarily selected. He points out that this arbitrariness is fine for a pure mathematician. But, according to him, an applied mathematician, faced with the reality of uncertainty in the real world, must take into account that world and cannot ignore the basic assumptions about uncertainty that underlie the probability calculus and reflect basic truths about the world.

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]

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 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]

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]

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]

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 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]

State-space models provide an important body of techniques for analyzing time series, but their use requires estimating unobserved states. The optimal estimate of the state is its conditional expectation given the observation histories, and computing this expectation is hard when there are nonlinearities. Existing filtering methods, including sequential Monte Carlo, tend to be either inaccurate or slow. In this paper, we study a nonlinear filter for nonlinear/non-Gaussian state-space models, which uses Laplace’s method, an asymptotic series expansion, to approximate the state’s conditional mean and variance, together with a Gaussian conditional distribution. This Laplace Gaussian filter (LGF) gives fast, recursive, deterministic state estimates, with an error which is set by the stochastic characteristics of the model and is, we show, stable over time. We illustrate the estimation ability of the LGF by applying it to the problem of neural decoding and compare it to sequential Monte Carlo both in simulations and with real data. We find that the LGF can deliver superior results in a small fraction of the computing time. This article has supplementary material online. [ABSTRACT FROM AUTHOR]

In this paper, we extend the LASSO method (Tibshirani 1996) for simultaneously fitting a regression model and identifying important interaction terms. Unlike most of the existing variable selection methods, our method automatically enforces the heredity constraint, that is, an interaction term can be included in the model only if the corresponding main terms are also included in the model. Furthermore, we extend our method to generalized linear models, and show that it performs as well as if the true model were given in advance, that is, the oracle property as in Fan and Li (2001) and Fan and Peng (2004). The proof of the oracle property is given in online supplemental materials. Numerical results on both simulation data and real data indicate that our method tends to remove irrelevant variables more effectively and provide better prediction performance than previous work (Yuan, Joseph, and Lin 2007 and Zhao, Rocha, and Yu 2009 as well as the classical LASSO method). [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]

We apply the nonconcave penalized likelihood approach to obtain variable selections as well as shrinkage estimators. This approach relies heavily on the choice of regularization parameter, which controls the model complexity. In this paper, we propose employing the generalized information criterion, encompassing the commonly used Akaike information criterion (AIC) and Bayesian information criterion (BIC), for selecting the regularization parameter. Our proposal makes a connection between the classical variable selection criteria and the regularization parameter selections for the nonconcave penalized likelihood approaches. We show that the BIC-type selector enables identification of the true model consistently, and the resulting estimator possesses the oracle property in the terminology of Fan and Li (2001). In contrast, however, the AIC-type selector tends to overfit with positive probability. We further show that the AIC-type selector is asymptotically loss efficient, while the BIC-type selector is not. Our simulation results confirm these theoretical findings, and an empirical example is presented. Some technical proofs are given in the online supplementary material. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new dimension reduction method by introducing a nominal regression model with the hazard function as the conditional mean, which naturally retrieves information from complete data and censored data as well. Moreover, without requiring the linearity condition, the new method can estimate the entire central subspace consistently and exhaustively. The method also provides an alternative approach for the analysis of censored data assuming neither the link function nor the distribution. Hence, it exhibits superior robustness properties. Numerical studies show that the method can indeed be readily used to efficiently estimate survival models, explore the data structures and identify important variables. [ABSTRACT FROM AUTHOR]

The technology to harvest electricity from wind energy is now advanced enough to make entire cities powered by it a reality. High-quality, short-term forecasts of wind speed are vital to making this a more reliable energy source. Gneiting et al. (2006) have introduced a model for the average wind speed two hours ahead based on both spatial and temporal information. The forecasts produced by this model are accurate, and subject to accuracy, the predictive distribution is sharp, that is, highly concentrated around its center. However, this model is split into nonunique regimes based on the wind direction at an offsite location. This paper both generalizes and improves upon this model by treating wind direction as a circular variable and including it in the model. It is robust in many experiments, such as predicting wind at other locations. We compare this with the more common approach of modeling wind speeds and directions in the Cartesian space and use a skew- t distribution for the errors. The quality of the predictions from all of these models can be more realistically assessed with a loss measure that depends upon the power curve relating wind speed to power output. This proposed loss measure yields more insight into the true value of each model’s predictions. [ABSTRACT FROM AUTHOR]

This note is based on an invited discussion of the article, “A Moving Average Approach for Spatial Statistical Models on Stream Networks” by Jay M. Ver Hoef and Erin E. Peterson. Ver Hoef and Peterson (hereafter VHP) have extended the idea of flow-related statistical dependence in streams to one where dependence may not respect flow, such as might happen when modeling data on fish in connected streams. We congratulate VHP for their innovative paper on using moving average models in stream networks. [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]

Lévy processes have been receiving increasing attention in financial modeling. One distinctive feature of such models is that their characteristic functions are readily available. Inference based on characteristic functions is very useful for studying Levy processes. By incorporating the recent advances in nonparametric approaches, empirical likelihood methods based on characteristic functions are developed in this paper for parameter estimation, testing a particular parametric class including the presence of a jump component in the Levy process and testing for symmetry of a distribution. Simulation and case studies confirm the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes several extensions of the concept of runs to the multivariate setup, and studies the resulting tests of multivariate randomness against serial dependence. Two types of multivariate runs are defined: (i) an elliptical extension of the spherical runs proposed by Marden (1999), and (ii) an original concept of matrix-valued runs. The resulting runs tests themselves exist in various versions, one of which is a function of the number of data-based hyperplanes separating pairs of observations only. All proposed multivariate runs tests are affine-invariant and highly robust: in particular, they allow for heteroscedasticity and do not require any moment assumption. Their limiting distributions are derived under the null hypothesis and under sequences of local vector ARMA alternatives. Asymptotic relative efficiencies with respect to Gaussian Portmanteau tests are computed, and show that, while Marden-type runs tests suffer severe consistency problems, tests based on matrix-valued runs perform uniformly well for moderate-to-large dimensions. A Monte Carlo study confirms the theoretical results and investigates the robustness properties of the proposed procedures. A real-data example is also treated, and shows that combining both types of runs tests may provide some insight on the reason why rejection occurs, hence that Marden-type runs tests, despite their lack of consistency, also are of interest for practical purposes. [ABSTRACT FROM AUTHOR]

This paper introduces an open-ended sequential algorithm for computing the p-value of a test using Monte Carlo simulation. It guarantees that the resampling risk, the probability of a different decision than the one based on the theoretical p-value, is uniformly bounded by an arbitrarily small constant. Previously suggested sequential or nonsequential algorithms, using a bounded sample size, do not have this property. Although the algorithm is open-ended, the expected number of steps is finite, except when the p-value is on the threshold between rejecting and not rejecting. The algorithm is suitable as standard for implementing tests that require (re)sampling. It can also be used in other situations: to check whether a test is conservative, iteratively to implement double bootstrap tests, and to determine the sample size required for a certain power. An R-package implementing the sequential algorithm is available online. [ABSTRACT FROM AUTHOR]

Quantile regression has emerged as a significant extension of traditional linear models and its potential in survival applications has recently been recognized. In this paper we study quantile regression with competing risks data, formulating the model based on conditional quantiles defined using the cumulative incidence function, which includes as a special case an analog to the usual accelerated failure time model. The proposed competing risks quantile regression model provides meaningful physical interpretations of covariate effects and, moreover, relaxes the constancy constraint on regression coefficients, thereby providing a useful, perhaps more flexible, alternative to the popular subdistribution proportional hazards model. We derive an unbiased monotone estimating equation for regression parameters in the quantile model. The uniform consistency and weak convergence of the resulting estimators are established across a quantile continuum. We develop inferences, including covariance estimation, second-stage exploration, and model diagnostics, which can be stably implemented using standard statistical software without involving smoothing or resampling. Our proposals are illustrated via simulation studies and an application to a breast cancer clinical trial. [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]

Right-censored time-to-event data are often observed from a cohort of prevalent cases that are subject to length-biased sampling, Informative right censoring of data from the prevalent cohort within the population often makes it difficult to model risk factors on the unbiased failure times for the general population, because the observed failure times are length biased. In this paper, we consider two classes of flexible semiparametric models: the transformation models and the accelerated failure time models, to assess covariate effects on the population failure times by modeling the length-biased times. We develop unbiased estimating equation approaches to obtain the consistent estimators of the regression coefficients. Large sample properties for the estimators are derived. The methods are confirmed through simulations and illustrated by application to data from a study of a prevalent cohort of dementia patients. [ABSTRACT FROM AUTHOR]

The aim of this paper is to develop an intrinsic regression model for the analysis of positive-definite matrices as responses in a Riemannian manifold and their association with a set of covariates, such as age and gender, in a Euclidean space. The primary motivation and application of the proposed methodology is in medical imaging. Because the set of positive-definite matrices do not form a vector space, directly applying classical multivariate regression may be inadequate in establishing the relationship between positive-definite matrices and covariates of interest, such as age and gender, in real applications. Our intrinsic regression model, which is a semiparametric model, uses a link function to map from the Euclidean space of covariates to the Riemannian manifold of positive-definite matrices. We develop an estimation procedure to calculate parameter estimates and establish their limiting distributions. We develop score statistics to test linear hypotheses on unknown parameters and develop a test procedure based on a resampling method to simultaneously assess the statistical significance of linear hypotheses across a large region of interest. Simulation studies are used to demonstrate the methodology and examine the finite sample performance of the test procedure for controlling the family-wise error rate. We apply our methods to the detection of statistical significance of diagnostic effects on the integrity of white matter in a diffusion tensor study of human immunodeficiency virus. Supplemental materials for this article are available online. [ABSTRACT FROM AUTHOR]

Regression quantiles can be substantially biased when the covariates are measured with error. In this paper we propose a new method that produces consistent linear quantile estimation in the presence of covariate measurement error. The method corrects the measurement error induced bias by constructing joint estimating equations that simultaneously hold for all the quantile levels. An iterative EM-type estimation algorithm to obtain the solutions to such joint estimation equations is provided. The finite sample performance of the proposed method is investigated in a simulation study, and compared to the standard regression calibration approach. Finally, we apply our methodology to part of the National Collaborative Perinatal Project growth data, a longitudinal study with an unusual measurement error structure. [ABSTRACT FROM AUTHOR]

Empirical likelihood has been found very useful in many different occasions. However, when applied directly to some more complicated statistics such as U-statistics, it runs into serious computational difficulties. In this paper, we introduce a so-called jackknife empirical likelihood (JEL) method. The new method is extremely simple to use in practice. In particular, the JEL is shown to be very effective in handling one and two-sample U-statistics. The JEL can be potentially useful for other nonlinear statistics. [ABSTRACT FROM AUTHOR]