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T. S. FERGUSON, L. S. SHAPLEY, and J. B. MACQUEEN (Eds.). Hayward, CA: Institute of Mathematical Statistics, 1996. ISBN 0-940600-42-0. xiv + 407 PP. $32 (P). This book is a [...]

Essays in Econometrics: Collected Papers of Clive W. J. Granger (Vols. 1 and 2).* Eric GHYSELS, Norman R. SWANSON, and Mark W. WATSON (Eds.). New York: Cambridge University Press, 2001. [...]

This festschrift in honor of Professor Le Cam's 70th birthday attests to the wide-ranging impact of his work in probability theory, specifically on convergence and contiguity of probability measures, superefficiency, [...]

The Bradley-Terry model for a paired-comparison experiment with t treatments postulates a set of t 'true' treatment ratings π1, π2, ..., π1 such that π1 is ≥ 0, σpi;i = 1 and the probability for preferring treatment i to treatment j is π2 (π2 + πj)-1. Thus, according to this model, every comparison of two treatments results in a definite preference for one of the two. This is an unrealistic restriction since when there is no difference between the responses due to two treatments, any method of expressing preference for one over the other is somewhat arbitrary. This paper considers a modification of the Bradley-Terry model by introducing an additional parameter, called threshold parameter, into the model. This permits 'ties' in the model. The problem of estimation and tests of hypotheses for the parameters of the modified model is also dealt with in the paper. [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 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 paper presents a novel data-driven bandwidth selector compatible with the small bandwidth asymptotics developed in Cattaneo, Crump, and Jansson (2009) for density-weighted average derivatives. The new bandwidth selector is of the plug-in variety, and is obtained based on a mean squared error expansion of the estimator of interest. An extensive Monte Carlo experiment shows a remarkable improvement in performance when the bandwidth-dependent robust inference procedures proposed by Cattaneo, Crump, and Jansson (2009) are coupled with this new data-driven bandwidth selector. The resulting robust data-driven confidence intervals compare favorably to the alternative procedures available in the literature. The online supplemental material to this paper contains further results from the simulation study. KEY WORDS: Averaged derivative; Bandwidth selection; Robust inference; Small bandwidth asymptotics.

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

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

Comments on a paper which developed a model for clustered functional data through a hierarchical nonparametric mixed-effects structure. Types of data that constitute clustered functional data; Features of the general nonparametric approach; Estimation methods.

A general method for estimating the distribution of a solution to an estimating equation defined through as sum of independent random variables is proposed. Suggested expansions are valid for the distribution of approximated parameters from general regression models and are not different from saddlepoint approximations in the case of iid random variables. A main advantage of the proposed methodology is that in requires on the conditional cumulant-generating function to be specified., 1. INTRODUCTION Daniels's (1954) seminal paper on saddlepoint approximations in statistics spawned a great deal of research in the general area of small-sample asymptotic approximations. His original paper concentrated primarily [...]

A data set consisting of 143 rankings of 10 occupations from a survey of Goldberg has been analyzed in a number of recent papers. The purpose of this paper is to use so-called 'nested orthogonal contrasts' of the occupations to gain further insight into the data. A contrast is a comparison of subsets of the occupations based on their relative ranks; contrasts are orthogonal if the comparisons they represent are not confounded. Various models based on sets of orthogonal contrasts-including contingency table models, models analogous to those of Fligner and Verducci, and latent class models--are applied to the data. It is found that there are three main groups of occupations based on overall prestige, and within each group are distinctions between managerial and technical occupations. KEY WORDS: Contingency tables; Discordant pairs; Kendall's tau; Mallows's [pi] model; Orthogonal contrasts; Permutations; Rank statistics., 1. BACKGROUND One question on a survey of engineering graduates discussed by Goldberg (1976) asked people to rank m = 10 occupations according to their perceived social prestige, with 1 [...]

The problem considered is the estimation of the population total of some characteristic from a simple random sample containing a few large or extreme observations. The effect of these large units in the sample is to distort the estimate of the population total. It is therefore important to correct the weights for such units or deflate their values at the estimation stage once they have been sampled and identified as unusually large units. In this paper, three estimators that alter the usual sampling weights have been considered. The efficiencies of these estimators have been worked out in terms of the ratio of the mean squared error of the usual estimator of the population total to the mean squared error of these estimators. A numerical study of these estimators is also discussed. [ABSTRACT FROM AUTHOR]

This article contains a bibliography of papers on multiple comparisons between 1966 and 1976. A. discussion of some of the more important developments during this period precedes the bibliography. [ABSTRACT FROM AUTHOR]

A multiple-choice item is called ideal if all its alternatives are equally attractive to every person who cannot answer the item correctly without guessing. This paper discusses reasons for attempting to construct ideal items, develops methods for testing whether items are ideal or at least more nearly ideal than other items, and presents examples of both ideal and nonideal items. [ABSTRACT FROM AUTHOR]

The purpose of this paper is the presentation of formulae for obtaining matrix derivatives of the second order to use in making tests for maxima and minima. The theory of such second order derivatives is presented. These formulae require the rearrangment of the parameter elements in vector form and the transformed results feature Kronecker products, which have certain desirable properties. Application is made to several types of problems. [ABSTRACT FROM AUTHOR]

In this paper the first two moments of the Statistic (treatment sum of squares)/(treatment +error sums of squares) over all possible random assignments of treatments to the experimental plots are obtained for two associate PBIB designs. They are compared with the corresponding moments of a central beta distribution to study the extent to which the normal theory test may serve as an approximation to the randomization test. It is found that the approximation is reasonable for some classes of PBIB designs. [ABSTRACT FROM AUTHOR]

In many scientific investigations, it is desired to bring together, or link, two or more documents which represent the same individual, even though these documents do not contain a unique identifier and were derived from different sources. In medical and public health research and elsewhere, this problem is known as the document linkage problem. This paper considers some aspects of classifying pairs of documents into one of two populations when their items are identifying information, where each item of information can take on three distinct values correct, incorrect or missing. Section I identifies three document linkage problems. Sections 2 and 3 deal with the mathematical formulation of the multivariate document linkage problem. Section 4 gives the classification procedure and Section 5 deals with the application of the theory to a problem in the field of public health. [ABSTRACT FROM AUTHOR]

Economic statisticians do not enjoy an untarnished reputation for accurate forecasting. We have managed, over the years, to come up with some memorable failures. While we have also had our share of successes, they are not as well remembered nor as numerous as we should like. Recently, however, we have begun to pay more attention to the record, and a substantial body of evidence on forecasting performance has accumulated. In this paper I propose to review this record, try to arrive at a balanced appraisal, and offer some suggestions for improvement. [ABSTRACT FROM AUTHOR]

This paper deals with methods of "cluster analysis". In particular we attack the problem of exploring the structure of multivariate data in search of "clusters". The approach taken is to use a computer procedure to obtain the "best" partition of n objects into g groups. A number of mathematical criteria for "best" are discussed and related to statistical theory. A procedure for optimizing the criteria is outlined. Some of the criteria are compared with respect to their behavior on actual data. Results of data analysis are presented and discussed. [ABSTRACT FROM AUTHOR]

This paper describes certain quota sampling procedures and attempts to show that they are very close to traditional probability sampling. Quotas are shown to depend on availability for interviewing and evidence is presented to show that sex, age, and employment status are reasonable predictors of availability. Quota sampling methods are not unbiased but data are presented which suggest that the bias is generally of the order of 3 to 5 per cent. It is shown, however, that the cost differentials between these quota samples and call-back samples are small. The major advantage of this new procedure may well be the speed with which interviewing may be completed during crises such as the Kennedy assassination. [ABSTRACT FROM AUTHOR]

In this paper we review the literature on the problem of handling multivariate data with observations missing on some or all of the variables under study. We examine the ways that statisticians have devised to estimate means, variances, correlations and linear regression functions from such data and refer to specific computer programs for carrying out the estimation. We show how the estimation problems can be simplified if the missing data follows certain patterns. Finally, we outline the statistical properties of the various estimators. [ABSTRACT FROM AUTHOR]

In this paper confidence bands are given for simple linear model. The confidence bands that are given are straight lines rather than curves and are either (1) parallel or (2) trapezoidal. The confidence bands are over a finite length interval. [ABSTRACT FROM AUTHOR]

A common problem in many areas is to achieve a combination of control variables which will simultaneously maximize all of the responses which are functions of the control variables. The fact that in general we can not simultaneously maximize all of the responses has led to the formulation of compromise solutions to this vector maximum problem. A point in the control variable space is better than a second point if each response at the first point is greater than or equal to the corresponding response at the second point. If a point is such that there is no better point, it is said to be admissible, or efficient. A set of points is complete if given any point not in the set there is a point in the set which is better. In this paper this formulation is used to consider the allocation of sample size to several strata when there are several characteristics of interest. [ABSTRACT FROM AUTHOR]

This paper considers some problems in the probabilistic analysis of physical evidence in criminal investigations. Two basic assumptions are made: (1) That the number of persons or objects possessing a particular set of properties can be considered as a random variable, and (2) that it is possible to estimate the probability function of this random variable. Two models (one with and one without the assumption that the suspect is a random selection from the set of possible suspects) which arc applicable to the evaluation of partial transfer evidence--an important category of physical evidence that is found in most criminal investigations--are developed. A detailed analysis of the models and an example are presented for the case when the estimated probability distribution is binomial with an expected value less than 1. As the expected value becomes smaller, the assumption of randomness in the selection of the suspect becomes immaterial to the evaluation of the evidential significance. [ABSTRACT FROM AUTHOR]

Our aim is to relax assumptions and simplify proofs in results given by Jones, Haran, Caffo, and Neath in the recent paper "Fixed-Width Output Analysis for Markov Chain Monte Carlo." [ABSTRACT FROM AUTHOR]