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AbstractLow-rank approximation is a popular strategy to tackle the “big n problem” associated with large-scale Gaussian process regressions. Basis functions for developing low-rank structures are crucial and should be carefully specified. Predictive processes simplify the problem by inducing basis functions with a covariance function and a set of knots. The existing literature suggests certain practical implementations of knot selection and covariance estimation; however, theoretical foundations explaining the influence of these two factors on predictive processes are lacking. In this paper, the asymptotic prediction performance of the predictive process and Gaussian process predictions are derived and the impacts of the selected knots and estimated covariance are studied. The use of support points as knots, which best represent data locations, is advocated. Extensive simulation studies demonstrate the superiority of support points and verify our theoretical results. Real data of precipitation and ozone are used as examples, and the efficiency of our method over other widely used low-rank approximation methods is verified. [ABSTRACT FROM AUTHOR]

We agree that converting data to similar resolutions would lose some statistical information from our data. We thank gratefully Professors Wei Tu, Bei Jiang, Linglong Kong, and Professor Sudipto Banerjee for their insightful comments and discussion of our paper. The inference of the occupancy status of houses sharing one location might require more information at the individual level, which is the primary data barrier in social science. [Extracted from the article]

It should, however, be noted that such approximations have ultimately allowed the authors to conduct a comprehensive analysis of thousands of images from multiple studies, which further substantiates their findings. We congratulate the authors on an interesting paper which combines the ideas of shape analysis with longitudinal data analysis. This, of course, loses some of the elegance of the SRNF framework, but at a considerable ease of preserving the topology of the data and avoiding Euclidean approximations. [Extracted from the article]

In these cases getting accurate confidence intervals is of first order importance, and the methods Ignatiadis and Wager develop are likely to be useful. I want to congratulate Nikolaos Ignatiadis and Stefan Wager on a very stimulating paper on a timely and important topic. [Extracted from the article]

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.

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.

This article presents the Markov chain Monte Carlo (MCMC) statistical technique. The impact on the discipline is deep and durable, because these methods have opened new horizons in the scale of the problems that one can deal with, thus enhancing the position of statistics in most applied fields. The MCMC revolution has in particular boosted Bayesian statistics to new heights by providing a virtually universal tool for dealing with integration problems. This can be seen in the explosion of papers dealing with complex models, hierarchical modelings, nonparametric Bayesian estimation, and spatial statistics. This trend has also created new synergies with mathematicians and probabilists, as well as econometricians, engineers, ecologists, astronomers, and others, for theoretical requests and practical implications of MCMC techniques. The main factor in the success of MCMC algorithms is that they can be implemented with little effort in a large variety of settings. This is obviously true of the Gibbs sampler, which provided some conditional distributions are available as shown by the BUGS software. We mentioned BUGS and CODA as existing software dedicated to MCMC algorithms but much remains to be done before MCMC becomes part of commercial software.

This article discusses the state of statistical process control as we proceed into the 21st century. SPC refers to some statistical methods used extensively to monitor and improve the quality and productivity of manufacturing processes and service operations. SPC primarily involves the implementation of control charts, which are used to detect any change in a process that may affect the quality of the output. The first control charts were developed by Walter A. Shewhart in the 1920s. These simple Shewhart charts have dominated applications to date. The process-monitoring problem can be described in general terms. Murphy's law explains the purpose monitoring: over time, something will inevitably change and possibly cause deterioration in process quality. The Shewhart charts were designed to make it relatively easy for process personnel without statistical training to set up, apply, and interpret the charts using only a pencil and paper for calculations. Bayesian procedures appear to be naturally suited for process monitoring. The standard approach to sampling for a control chart is to use a fixed sampling rate in which samples of fixed size are obtained using a fixed-length sampling interval.

The article presents information on a study which described capture-recapture models for the estimation of demographic parameters of wild animal populations. The capture-recapture models are now also widely used in a variety of other applications such as the census undercount, incidence of disease, criminality, homelessness and computer bugs. Although they have their historical roots in the twentieth century, capture-recapture models are basically a twentieth century phenomenon. Often capture-recapture studies have a long duration, rendering the closed models impractical. Thus there has been a need for the development of models that allow for additions and deletions. Another focus of research has been to develop combinations of different sampling methods. One early example used a robust design that combines both open and closed models in one analysis. Since then many papers have used this design for many reasons, for example, to allow for unequal catchability, to separate recruitment from immigration and to estimate temporary emigration.

Consider a finite sample from an unknown distribution over a countable alphabet. The missing mass refers to the probability of symbols that do not appear in the sample. Estimating the missing mass is a basic problem in statistics and related fields, which dates back to the early work of Laplace, and the more recent seminal contribution of Good and Turing. In this article, we introduce a generalized Good-Turing (GT) framework for missing mass estimation. We derive an upper-bound for the risk (in terms of mean squared error) and minimize it over the parameters of our framework. Our analysis distinguishes between two setups, depending on the (unknown) alphabet size. When the alphabet size is bounded from above, our risk-bound demonstrates a significant improvement compared to currently known results (which are typically oblivious to the alphabet size). Based on this bound, we introduce a numerically obtained estimator that improves upon GT. When the alphabet size holds no restrictions, we apply our suggested risk-bound and introduce a closed-form estimator that again improves GT performance guarantees. Our suggested framework is easy to apply and does not require additional modeling assumptions. This makes it a favorable choice for practical applications. for this article are available online. [ABSTRACT FROM AUTHOR]

In this paper we are concerned with inferences from a sample survey to a finite population. We contrast inferences that are dependent on an assumed model with inferences based on the randomization induced by the sample selection plan. Randomization consistency for finite population estimators is defined and adopted as a requirement of probability sampling. A numerical example is examined to illustrate the dangers in the use of model-dependent estimators even when the model is apparently consonant with the sample data. The paper concludes with a summary of principles that we believe should guide the practitioner of sample surveys of finite populations. [ABSTRACT FROM AUTHOR]

In this article, the author comments on the research paper of John J. Wiorkowski titled "Estimating Volumes of Remaining Fossil Fuel Resources: A Critical Review," published in the September 1981 issue of "Journal of the American Statistical Association." According to the author, the strength of Wiorkowski's paper is in bringing the important problem of petroleum resource estimation to the attention of statisticians. The major weaknesses are in the organization and classification of models and the gaps in coverage. The major issues in resource estimation that Wiorkowski discusses are models for estimating the total oil and gas remaining to be found and a closely related problem, estimating the amount of appreciation in known fields. The problem with the discussion of the models is the lack of a proper classification scheme. Although Wiorkowski mentions the model of researchers E. Barouch and G.M. Kaufman, he fails to note that it is one of a general class of models that are based on the discovery process and fails to emphasize that it is a play model, whereas the others he discusses are used at a higher level of aggregation.

The article presents the author's comments on paper by researcher D. Basu related to randomization analysis of experimental data. Basu writes entertainingly, perhaps, but not informatively. Basu's paper discusses prerandomization, postrandomization, and unrecorded randomization. This discussion is irrelevant. But it is useful, perhaps, to make a remark. It also discusses the sufficiency principle. As Basu has written, this is a data-reduction principle. Basu also discusses researcher R.A. Fisher randomization test. It is obvious that the population in a randomization test of a randomized experiment is "the product of the statistician's imagination." With respect to Basu's writing on "the physical act of randomization," the author believes Basu is merely plain wrong. The paper also describes randomized pair trial. In his paper, Basu gives a hypothetical interchange of a statistician and a scientist and the author. The author suggests that this serves no useful purpose. The author finds the lack of knowledge that underlies Basu's thesis rather surprising, incongruous, and deplorable.

The author is pleased to discuss a paper on the estimation of probability density functions and the location of bumps. There is an extensive literature on density estimation, but many statisticians seem doubtful about the usefulness of these techniques because their application seems subjective and complicated. A major criticism the author would make of this paper is that it does not help to dispel this negative attitude of statisticians toward density estimation. One cannot help but be impressed by the ingenuity of I. J. Good and R. A. Gaskins and even to believe that they may be able to successfully fit probability densities to data. The existence of bumps at the extremes of a sample can be investigated for large sample sizes by treating the bottom and top ends of the original sample as two new samples to be analyzed by themselves. Statistical scientists should heed the flippant advice of Sir Arthur Eddington: "Never trust an experimental result until it has been confirmed by theory."

Bayesian techniques are widely used in these days for simultaneous estimation of several parameters in compound decision problems. Often, however, the main objective is to produce an ensemble of parameter estimates whose histogram is in some sense close to the histogram of population parameters. This is for example the situation in subgroup analysis, where the problem is not only to estimate the different components of a parameter vector, but also to identify the parameters that are above, and the others that are below a certain specified cutoff point. We have proposed in this paper Bayes estimates in a very general context that meet this need. These estimates are obtained by matching the first two moments of the histogram of the estimates, and the posterior expectations of the first two moments of the histogram of the parameters, and minimizing, subject to these conditions, the posterior expectation of the Euclidean distance between the estimates and the parameters. Several applications of the main result are provided in the normal and other models. Also, the results are applied to an actual data set. [ABSTRACT FROM AUTHOR]

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.

This article presents a response to several commentaries regarding a study which proposed computations for Bayesian p values in composite null models. In the double use of data and conditioning, Michael Evans and Hal S. Stern both discussed what constitutes double use of the data in computing a p value. They take opposite perspectives on this issue. Evans argues that the only way to avoid double use of the data is to separate the data into two independent subsets, using one subset to fit the model and the other to assess the validity of the model. Because the procedures that we recommend do not formally split the data into two parts, Evans suggests that they can be guilty double use of the data. In contrast, Stern does not feel that it is necessary to worry about double use of the data the extent that we worry, he does not feel that even the posterior predictive p value involves double use of the data. These contrasting positions perfectly highlight what we view to be the main motivation for our paper. We feel that it is very important to avoid a double use of the data, but that separating the data into two independent subsets is a too drastic solution that can lose considerable power. We consider each of these issues in turn.

The author offers a commentary on an article by Professors J. Duchi et al which developed packing arguments and perturbation mechanisms for differential privacy in the minimax framework for statistical estimation leading to a range of minimax optimal estimation rates. He discusses the prevalent models for designing differentially private algorithms, how minimax lower bounds are developed, and the attention received by the sequence of papers by the authors in the machine learning community.

In the present article, Dai et al. ([5]) studies FDR control of the GM and DS methods for generalized linear models (GLMs) under a unified framework. Specifically, Xing, Zhao, and Liu ([16]) develops the Gaussian Mirror (GM) method for controlling FDR in high-dimensional linear regressions. Wang and Ramdas ([15]) uses e-value and develops the e-BH procedure to control FDR. With the maturity of data collection techniques, the analysis of data with high-dimensional input is now routinely conducted. [Extracted from the article]

Modern scientific studies often collect datasets in the form of tensors. These datasets call for innovative statistical analysis methods. In particular, there is a pressing need for tensor clustering methods to understand the heterogeneity in the data. We propose a tensor normal mixture model approach to enable probabilistic interpretation and computational tractability. Our statistical model leverages the tensor covariance structure to reduce the number of parameters for parsimonious modeling, and at the same time explicitly exploits the correlations for better variable selection and clustering. We propose a doubly enhanced expectation–maximization (DEEM) algorithm to perform clustering under this model. Both the expectation-step and the maximization-step are carefully tailored for tensor data in order to maximize statistical accuracy and minimize computational costs in high dimensions. Theoretical studies confirm that DEEM achieves consistent clustering even when the dimension of each mode of the tensors grows at an exponential rate of the sample size. Numerical studies demonstrate favorable performance of DEEM in comparison to existing methods. [ABSTRACT FROM AUTHOR]

In this article the author presents his views related to the comments on his research paper entitled "Parametric Empirical Bayes Inference: Theory and Applications," by various statisticians. The author feel himself honored to have six such distinguished statisticians share their thoughts on this article. All think deeply about the foundations of statistics, as well as its methods. They seem to agree that procedures like those proposed in this paper are underutilized. He remarks that many of the commenter discuss his paper primarily in terms of its relationship to Bayesian thinking. It will be easiest for the author to discuss the general Bayes empirical Bayes issue before turning to more detailed comments. Empirical Bayes says that if the class II of all possible prior distributions contains more than one prior, then the inference rule should do well against the entire range of priors in II. He says that the statisticians need not choose between the Bayesian and frequentist, or between the Bayesian and empirical Bayesian viewpoints. All viewpoints have something to offer, none being adequate in itself Bayesians are right

The author expresses his delightment on somewhat haphazard survey of discrimination law and statistical analysis, that has sparked some controversy. The author responds to some of the criticism. Lea Brilmayer, in a discussion makes two major points that author's description of legal doctrine is not organized around the phrases "disparate treatment"; and that his legal analysis rejects discriminatory intent as an essential element of discrimination. Author's paper identified four points at which discrimination can occur. The first three involve "disparate treatment." At no point did he maintain that disparate treatment pertains only to "a decision that purports to be ad hoc." As indicated, the concept also pertains to a facially neutral rule applied in a discriminatory fashion, and he should now add that discrimination in the formulation of a rule is another version of disparate treatment. The final category of cases does not involve discriminatory treatment, but rather disparate impact, as the paper itself noted.

The article presents author's comments on paper entitled "Representing Points in Many Dimension by Trees and Castles." On closer inspection, though, the author finds that their method really comprises two separate ideas. The paper does not make this distinction, but, by doing so, he will show it is possible to isolate the better idea and use it by itself to good effect. There are two steps one must go through to construct a two-dimensional graphical display for multidimensional data points; first, one must choose a two-dimensional graphical symbol and then one must assign the coordinates of the multidimensional data to the parameters that describe the construction of that symbol. B. Kleiner and J.A. Hartigan's method can be decomposed into a way to perform each of these two steps; for the first, they choose trees or castles as the display; for the second, they assign the data coordinates to the tree or castle construction parameters in a way designed to depict an hierarchical organization obtained from clustering the coordinates.

The article presents the authors' comments on researcher D. Basu's paper related to randomization analysis of experimental data. Basu's paper on researcher R.A. Fisher's randomization test for experimental data (FRTED) is certainly entertaining. Although much of the paper is devoted to the thesis that Fisher changed his views on FRTED, apparently the primary point of the paper is to argue that FRTED is "not logically viable." Admittedly, FRTED is not the ultimate statistical weapon, even in randomized experiments, but calling it illogical is rather bizarre. Basu criticizes FRTED through two primary arguments. His first line of criticism follows from his attack on a nonparametric test labeled as "Fisher's randomization test." Basu's second line of criticism of FRTED takes the form of a discussion between a statistician and a scientist. The author sees nothing illogical about the FRTED, it is relevant for those rare situations when a purely confirmatory test of a priori sharp hypothesis is to be made using a priori defined statistic having an associated priori definition of extremeness. FRTED cannot adequately handle the full variety of real data problems that practicing statisticians face when drawing causal inferences, and for this reason it might be illogical to try to rely solely on it in practice.

The article presents the author's comments on researcher D. Basu's paper related to randomization analysis of experimental data. Basu has provided researchers with an interesting and provocative critique of significance tests related to randomized experiments. It does seem to be true that there is not a unified mathematical theory of significance tests developed by researcher R.A. Fisher. Nevertheless, it is important to point out a fallacy in Basu's criticism of nonunique significance level. After confessing to a "ruthless cross-examination" of the wrong topic, the non-Fisherian nonparametric tests, Basu suggests that Fisher's silence in 1956 may be used to condemn the randomization test. The empirical evidence confronting Fisher certainly suggested the necessity of randomization in most field experiments, if the standard methods of analysis were to be used. The final substantial issue of Basu's paper is that of the ancillarity of the design outcome. Technically Basu is quite correct, if the randomization has validated a parametric model, the design outcome is then ancillary by design. It would, however, be as well not to forget the purpose of an ancillary statistic, since other definitions.

This article presents the views of the author on a paper by Roscoe R. Braham, Jr. which focused on involvement of statisticians in weather modification work. At two or three points in Braham's paper, distinctions are made between physical and statistical experiments (and observational programs), or between physical and statistical modes of thought. The comparison is sometimes to the discredit of statistics. In one broad sense of the word "statistics," such a distinction is otiose, for the meteorologist certainly makes inferences from quantitative data and thus does statistics, whether or not the word is used. So presumably some narrower sense of "statistics" is intended. Another sense in which the distinction might be intended is that of divergence between the result of a conventional statistical analysis, perhaps a significance test, on the one hand, and standard physical knowledge or possibly the intuition of one or more meteorologists on the other hand. Certainly cumulative scientific theory and the intuitions of scientists should be given great weight; yet scientific intuitions often vary widely, and there are many cases in which accepted doctrine has turned out to be wrong, sometimes after carrying out controlled randomized trials.

In this article the author comments on the research paper entitled "The Design and Analysis of the Observational Study--A Review," by Sonja M. McKinlay. The author remarks that although MeKinlay devotes a large part of her review to the developments in the analysis and interpretation of contingency tables, she refers the readers to papers by other statisticians too, for a historical perspective. Since the loglinear model approach now dominates the statistical literature on contingency table analysis, one often seem to ignore the ideas of statistician K. Pearson, which according to the author is a mistake. While the multivariate generalizations of the statisticians cross-product ratio or loglinear model approach were fermenting, the technique of standardization to eliminate the effects of categorical covariates received considerable attention in the epidemiological literature. The major advances in the literature on multidimensional contingency tables in the 1960's coincided with the emergence of interest in and the availability of high-speed computers, and this work received substantial impetus from several large-scale data analysis projects.

This article honors Morris H. DeGroot, who died November 2, 1989. It contains his last paper, which was being written at the time of his death. DeGroot was the founding editor of Statistical Science, which published an issue in 1991 in his honor. Morrie was a Bayesian. This special section of the periodical is formulated with a Bayesian focus to honor him. This issue of the periodical is a tribute to his life's works that a Bayesian theme section can be assembled within an issue without resorting to a special solicitation.

One fundamental statistical question for research areas such as precision medicine and health disparity is about discovering effect modification of treatment or exposure by observed covariates. We propose a semiparametric framework for identifying such effect modification. Instead of using the traditional outcome models, we directly posit semiparametric models on contrasts, or expected differences of the outcome under different treatment choices or exposures. Through semiparametric estimation theory, all valid estimating equations, including the efficient scores, are derived. Besides doubly robust loss functions, our approach also enables dimension reduction in presence of many covariates. The asymptotic and non-asymptotic properties of the proposed methods are explored via a unified statistical and algorithmic analysis. Comparison with existing methods in both simulation and real data analysis demonstrates the superiority of our estimators especially for an efficiency improved version. for this article are available online. [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.

This month marks the 100th anniversary of the appearance of William Sealey Gosset's celebrated article, "The Probable Error of a Mean" (Student 1908a). Gosset's elegant result represented the first in a series of exact, "small-sample" results that were developed by Gosset, Fisher, and others to form a central component of the modern theory of statistical inference. This review celebrates the centenary of Gosset's article by discussing both its background and its impact on statistical theory and practice. [ABSTRACT FROM AUTHOR]

In this paper, we highlight properties of Bayesian models in which the prior puts positive mass on all Kullback-Leibler neighborhoods of all densities. These properties are concerned with model choice via the Bayes factor, density estimation and the maximization of expected utility for decision problems. In four illustrations we focus on the Bayes factor and show that whatever models are being compared, the [log(Bayes factor)]/[sample size] converges to a non-random number which has a nice interpretation. A parametric versus semiparametric model comparison provides a fifth illustration. [ABSTRACT FROM AUTHOR]

Model selection is an important part of any statistical analysis and, indeed, is central to the pursuit of science in general. Many authors have examined the question of model selection from both frequentist and Bayesian perspectives, and many tools for selecting the "best model" have been suggested in the literature. This paper considers the various proposals from a Bayesian decision-theoretic perspective. [ABSTRACT FROM AUTHOR]

We review the most important statistical ideas of the past half century, which we categorize as: counterfactual causal inference, bootstrapping and simulation-based inference, overparameterized models and regularization, Bayesian multilevel models, generic computation algorithms, adaptive decision analysis, robust inference, and exploratory data analysis. We discuss key contributions in these subfields, how they relate to modern computing and big data, and how they might be developed and extended in future decades. The goal of this article is to provoke thought and discussion regarding the larger themes of research in statistics and data science. [ABSTRACT FROM AUTHOR]

In 1975, John W. Tukey defined statistical data depth as a function that determines the centrality of an arbitrary point with respect to a data cloud or to a probability measure. During the last decades, this seminal idea of data depth evolved into a powerful tool proving to be useful in various fields of science. Recently, extending the notion of data depth to the functional setting attracted a lot of attention among theoretical and applied statisticians. We go further and suggest a notion of data depth suitable for data represented as curves, or trajectories, which is independent of the parameterization. We show that our curve depth satisfies theoretical requirements of general depth functions that are meaningful for trajectories. We apply our methodology to diffusion tensor brain images and also to pattern recognition of handwritten digits and letters. for this article are available online. [ABSTRACT FROM AUTHOR]

One example is of course Graph HT ht . I want to first reemphasize that there is nothing special about the original population (Graph HT ht ) with regard to curvature: it may better, it may be worse. There appears to be no method that adapts to each setting except for the oracle Graph HT ht method, which is of course not implementable. The flat-value-surface example that LLL pose at the end of their Section 2.2 can happen for I w i = I w i SB 0 sb just as much as it can happen for Graph HT ht . [Extracted from the article]

Introducing some notation, let us define an empirical distribution with values Graph HT ht as Graph HT ht , where we let I SB a sb i denote point mass at a value I a i . Suppose one wishes to obtain predictions now based on Graph HT ht . Then we begin by splitting treated individuals (of size Graph HT ht ) into training and test samples of size I n SB a sb i and I n SB b sb i , respectively, where Graph HT ht . [Extracted from the article]

Many authors have dealt with the problem of extending ordinary two-sample rank tests to cases where censoring occurs. Albers and Akritas (1987) proposed simple tests for this purpose, based on the idea of making separate rankings for uncensored and censored observations and subsequently combining the resulting two rank statistics. Similarly, some papers appeared that studied the problem of censoring for the paired-data case rather than the two-sample case. This article indicates how the approach of Albers and Akritas can be adapted to the paired-data case. The tests involved are not based on the ranks of the differences, but the differences of the ranks in the pooled sample. In this way, use is made of interblock information. The asymptotic distribution of the new statistic is obtained under the null hypothesis and contiguous location alternatives. By way of example, Wilcoxon- and Savage-type scores are introduced that are optimal for logistic location and exponential scale alternatives, respectively. The two corresponding tests are applied to some real data, and comparisons are made with the results obtained with competing tests on the same data set. [ABSTRACT FROM AUTHOR]

The problem of obtaining A-optimal designs for comparing v test treatments with a control in b blocks of size k each is considered. A condition on the parameters (v, b, k) is identified for which optimal step-type designs can be obtained. Families of such designs are given. Methods of searching for highly efficient designs are proposed for situations in which it is difficult to determine an A-optimal design. Under the usual additive homoscedastic model, an A-optimal design minimizes the average variance of the least squares estimators of the control-test treatment comparisons. Majumdar and Notz (1983) gave a method for finding A-optimal designs. Their optimal designs can basically be of two types, using the terminology of Hedayat and Majumdar (1984): rectangular (R), in which every block has the same number of replications of the control, and step (S), in which some blocks contain the control t times and the others t + 1 times. Optimal R-type designs were studied by Hedayat and Majumdar (1985). Families of such designs, particularly when each block has one replication of the control, were given in that paper. In this article, we intend to study optimal S-type designs. Step-type designs are more complicated than rectangular-type designs; the latter are balanced incomplete block designs in the test treatments augmented by an equal number of controls in each block, but the former do not have such a simple characterization. Consequently, both the optimality and the construction of such designs are more involved. [ABSTRACT FROM AUTHOR]

The minimum norm quadratic unbiased estimator type (MINQUE type) of estimates considered in this article are obtained by requiring identical values for the ratios of the a priori variances to the a priori error variance and letting this common value tend to infinity. The resulting estimates are invariant quadratic unbiased estimators with certain parametric and nonparametric optimality properties: assuming normally distributed random effects the efficiency of the proposed estimates to the minimum variance quadratic unbiased estimates (MIVQUE's) approaches unity when the true variance ratios are identical and tend to infinity. Assuming nonnormal effect distributions in the model with two variance components, the estimates are asymptotically efficient: in a sequence of designs where the number of classes and the number of observations on each class approach infinity, it is shown that the asymptotic variances of the estimates are equivalent to the theoretical minimum variances for invariant quadratic unbiased estimators. The result is interesting and useful since the usual analysis of variance (ANOVA) estimate of between-classes variance has strictly larger asymptotic variance for the unbalanced one-way model. Commonly considered estimates result from this procedure; the usual residual mean square (assuming that all non-error effects are fixed) is the resulting estimate of the error variance. In the one-way model the resulting estimates coincide with estimates considered by Thomas and Hultquist (1978), Burdick and Graybill (1984), Ahrens, Kleffe, and Tenzler (1981), and Kaplan (1982). In particular, the convergence of the MINQUE estimates was proved in the latter two papers in the context of the unbalanced one-way model. The procedure yields computationally convenient estimates in the general mixed ANOVA model. Computing formulas are... [ABSTRACT FROM AUTHOR]

The two-dimensional controlled selection problem and the problem of maximizing the overlap of old and new primary sampling units after restratification and change of selection probabilities have been studied for several decades but have never been completely solved until now. Using transportation theory, complete solutions are obtained here for these and other problems. The solution to the controlled selection problem is based on a specific transportation model that was originally developed, in a previous paper by Cox and Ernst (1982), to solve completely the controlled rounding problem, namely the problem of optimally rounding real-valued entries in a two-way tabular array to adjacent integer values in a manner that preserves the tabular (additive) structure of the array. This model is also applied to other statistical problems, such as raking and statistical disclosure for frequency count tabulations and microdata. [ABSTRACT FROM AUTHOR]

The article presents a rejoinder to comments made on their article "A Statistical Model for Position Emission Tomography." Being a very active, multidisciplinary, field of research, it is hard to keep track of who suggested what and in what context, so in attempting to answer scholar Donald B. Rubin's question we are likely to overlook some contributors. The first use of a pixel model for an organ appeared in scholar G.N. Hounsfield's original development of X-ray computerized tomography. In 1978 scholars gave a short account of this early development in the field, including images produced using Hounsfield's algorithms. The fact that the physics of Position Emission Tomography (PET) is different, and inherently more stochastic, than that of X-ray transmission tomography has been common knowledge. Realizing that the additional randomness of PET calls for a more statistical way of thinking, scholars A.J. Rockmore and A.Macovski suggested estimating the emission density in PET, using a maximum-likelihood approach. Their paper fell short of identifying the connection between the tube count and the emission density. This omission on their part is probably a result of being unaware of the development of statistical methods for incomplete data.

The article presents authors' reply comments on various papers related to nonexperimental data and estimation of structural effects. Authors thank researcher John Geweke for his instructive comments and in reply only want to make sure that the relation between Geweke's third paragraph and authors' article is correctly understood. Authors' language did suggest, however, that meaningful statements about correlation with excluded variables would usually involve a very large sufficient set and in the case, authors find Geweke's example instructive. In response to the comment of researcher A.P. Dawid, authors are glad that he likes parts of their, but authors disagree with Dawid's comment on observational studies. Authors feel that selection of observations is not the important new feature in observational studies. The one and only new feature that is important is that the "treatments" or "factors" are not randomized. Selection of observations is not even new, because missing values can make estimates of causal effects inconsistent even when treatments are randomized.

The article comments on the paper by Murray Aitkin, Nan Laird and Brian Francis which presents an analyses of survival of patients in the Stanford Heart Transplantation Program, published in the June 1983 issue of the "Journal of the American Statistical Association." The author congratulates the authors for their careful and thorough analysis of the Stanford heart transplant survival data. There are many statistical issues involved in this area, and also many important medical and ethical questions. The comments are concentrated on the statistical problems, returning only briefly at the end to the current activity regarding larger societal concerns with heart transplantation. Aitkin, Laird, and Francis have made a number of choices in their approach to this reanalysis, and the author would like to comment on several of them. Each transition is examined separately. Aitkin, Laird, and Francis are careful to analyze waiting time for a heart, pretransplant survival, and post-transplant survival separately, before proceeding to comparisons. In particular, this approach enables them to detect a trend in pretransplant survival with calendar time of acceptance, more recent patients being the more healthy. This is an important complication for any assessment of trends in post-transplant survival. However, more could have been done along these lines.

The article comments on the paper by Murray Aitkin, Nan Laird and Brian Francis which presents an analyses of survival of patients in the Stanford Heart Transplantation Program, published in the June 1983 issue of the "Journal of the American Statistical Association." The author always approaches an article that purports to consider an analysis of a classical data set with a great deal of interest. He wonders: "Will the authors be able to discover new and useful results that others have been unable to detect in the past?" Of course, authors take a chance using a popular data set to demonstrate their new methodology. The problem is that perhaps the data set really does not have too much going for it in the first place even though the authors' new approach to analysis may have merit. Such may be the case here. When an experimenter visits with a statistical consultant concerning a proper experimental design to investigate the effectiveness of a new treatment, the consultant is called on to propose valid methods for demonstrating the repeatability of the effect of the new treatment over the standard one. Students in beginning courses in experimental design often have trouble understanding the concept and importance of replication. As statisticians they need to be sure that they do not overlook this concept as it applies to verification of a new statistical methodology. In this article, of course, the authors have chosen to emphasize the analysis of a classic data set rather than the evaluation of a new methodology, a task that can not be done on one data set.

In a graphical procedure for comparing k treatment means in a one-way ANOVA, one displays uncertainty intervals around the sample means and judges any pair to be significantly different if and only if their uncertainty intervals do not overlap. A graphical procedure is a Multiple Comparison Procedure (MCP) if and only if it controls the experimentwise error rate. In this paper we consider some new graphical MCP's for the unbalanced one-way ANOVA design. These procedures are based on different approximations to the Tukey-Kramer (TK) procedure (e.g., Kramer 1956). As such, they constitute alternatives to Gabriel (1978) (and its modification by Andrews, Snee, and Sarner 1980), which is based on approximating a less efficient MCP (the GT2 of Hochberg 1974). Two of the four procedures considered here are based on best and simple upper bounds to all the confidence-interval lengths of the TK method and hence must be conservative. The other two procedures are based on approximations (here too we have the best vs. the simple procedure), but simulations were used to find that their true experimentwise error rates are less than the nominal ones; that is, these procedures are still on the conservative side. The choice of a particular procedure will depend then on the relative importance of simplicity, efficiency, and the security of having a controlled experimentwise error rate. [ABSTRACT FROM AUTHOR]

This paper gives a derivation of the most powerful scale and location invariant test of normal versus Cauchy. A simulation study of this test shows that in testing normality versus symmetric stable alternatives it comes closer to being uniformly more powerful than any of five tests previously studied. [ABSTRACT FROM AUTHOR]

This paper presents a piecewise regression method for continuous models containing max or min operators, or both. This method does not require knowledge of the zone in which a shift in regimes occurs. Moreover, it allows the application of analytical derivatives to maximize the likelihood function, which greatly simplifies the estimation of the model. The method proposed exhibits fast convergence and can be used for an arbitrary number of regimes and variables. [ABSTRACT FROM AUTHOR]

In this article, the author comments on the research paper of John J. Wiorkowski titled "Estimating Volumes of Remaining Fossil Fuel Resources: A Critical Review," published in the September 1981 issue of "Journal of the American Statistical Association." Wiorkowski has tendered a critique of some of the statistical models used for estimating domestic and worldwide resources of oil and gas. The models Wiorkowski reviews were intended to answer a wide variety of questions. Among the quantities they were designed to estimate are resources in a single geologic basin, resources in a single play, total domestic resources, resources of frontier basins elsewhere in the world, total world resources, and even the payoff of continuing to explore a geologic basin that has already been drilled to a considerable degree. The most critical omissions are models of the discovery of crude oil as a function of time and of exploratory drilling effort that have been developed considerably beyond the stage surveyed by Wiorkowski. One of the most important new statistical methodologies overlooked by Wiorkowski, one that represents an entirely new approach for the statistician, is the elaborate subjective-estimation study of domestic resources conducted by the U.S. geological survey.