This monograph contains a comprehensive account of the recent work of the authors and other workers on large sample optimal inference for non-ergodic models. The non-ergodic family of models can be viewed as an extension of the usual Fisher-Rao model for asymptotics, referred to here as an ergodic family. The main feature of a non-ergodic model is that the sample Fisher information, appropriately normed, converges to a non-degenerate random variable rather than to a constant. Mixture experiments, growth models such as birth processes, branching processes, etc., and non-stationary diffusion...

About forty years ago, Richard von Mises proposed a theory for the analysis of the asymptotic behavior of nonlinear statistical functionals based on the differentiability properties of these functionals. His theory was largely neglected until the late 1960's when it experienced a renaissance due to developments in the field of robust statistics. In particular, the "Volterra" derivative used by von Mises evolved into the influence curve, which was used to provide information about the sensi ti vity of an estimator to outliers, as well as the estimator's asymptot ic variance. Moreover, with the...

In these notes some results are presented for the asymptotic behavior of the bootstrap procedure. Bootstrap is a procedure for estimating (approximating) the distribution of a statistic. It is based on resampling and simulations. It was been introduced in Efron (1979) and in the last decade it has been discussed for a wide variety of statistical problems. Introductory are the articles Efron and Gong (1983) and Efron and Tibshirani (1986) and the book Helmers (1991b). Many applications of bootstrap are discussed in Efron (1982). Survey articles are Beran (1984b), Hinkley (1988), and Diciccio...

In June of 1990, a conference was held on Probablity Models and Statisti cal Analyses for Ranking Data, under the joint auspices of the American Mathematical Society, the Institute for Mathematical Statistics, and the Society of Industrial and Applied Mathematicians. The conference took place at the University of Massachusetts, Amherst, and was attended by 36 participants, including statisticians, mathematicians, psychologists and sociologists from the United States, Canada, Israel, Italy, and The Nether lands. There were 18 presentations on a wide variety of topics involving ranking data....

This book is a concise presentation of the normal distribution on the real line and its counterparts on more abstract spaces, which we shall call the Gaussian distributions. The material is selected towards presenting characteristic properties, or characterizations, of the normal distribution. There are many such properties and there are numerous rel evant works in the literature. In this book special attention is given to characterizations generated by the so called Maxwell's Theorem of statistical mechanics, which is stated in the introduction as Theorem 0.0.1. These characterizations are...

The aim of this book is to make a comprehensive review on some of the research topics in the area of survey sampling which has not been covered in any book yet. The proposed book aims at making a comprehensive review of applications of Bayes procedures, Empirical Bayes procedures and their ramifications (like linear Bayes estimation, restricted Bayes least square prediction, constrained Bayes estimation, Bayesian robustness) in making inference from a finite population sampling. Parimal Mukhopadhyay is Professor at the Indian Statistical Institute (ISI), Calcutta. He received his Ph.D. degree...

Researchers in many disciplines now face the formidable task of processing massive amounts of high-dimensional and highly structured data. Advances in data collection and information technologies have coupled with innovations in computing to make commonplace the task of learning from complex data. As a result, fundamental statistical research is being undertaken in a variety of different fields. Driven by the difficulty of these new problems, and fueled by the explosion of available computer power, highly adaptive, non-linear procedures are now essential components of modern data analysis, a...

Author-approved bcc: Robust statistics and the design of experiments are two of the fastest growing fields in contemporary statistics. Up to now, there has been very little overlap between these fields. In robust statistics, robust alternatives to the nonrobust least squares estimator have been developed, while in experimental design, designs for the efficient use of the least square estimator have been developed. This volume is the first to link these two areas by studying the influence of the design on the efficiency and robustness of robust estimators and tests. It shows that robust...

The mathematical theory of ondelettes (wavelets) was developed by Yves Meyer and many collaborators about 10 years ago. It was designed for ap proximation of possibly irregular functions and surfaces and was successfully applied in data compression, turbulence analysis, image and signal process ing. Five years ago wavelet theory progressively appeared to be a power ful framework for nonparametric statistical problems. Efficient computa tional implementations are beginning to surface in this second lustrum of the nineties. This book brings together these three main streams of wavelet theory....

Since the 1950s, the pines native to the San Bernardino Mountains in Southern California have shown symptoms of decline that have proven to result from exposure to ozone, a major plant-damaging gas in photochemical oxidant air pollution. Because of their proximity to major urban areas, the San Bernardino Mountains have served as a natural laboratory for studying effects of oxidant and acidic air pollution on a mixed-conifer forest. This volume presents a body of research conducted over more than thirty years, including an intensive interdisciplinary five-year study begun in 1991. Chapters...