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Mik16s Cs6rgO and David M. Mason initiated their collaboration on the topics of this book while attending the CBMS-NSF Regional Confer ence at Texas A & M University in 1981. Independently of them, Sandor Cs6rgO and Lajos Horv~th have begun their work on this subject at Szeged University. The idea of writing a monograph together was born when the four of us met in the Conference on Limit Theorems in Probability and Statistics, Veszpr~m 1982. This collaboration resulted in No. 2 of Technical Report Series of the Laboratory for Research in Statistics and Probability of Carleton University and University of Ottawa, 1983. Afterwards David M. Mason has decided to withdraw from this project. The authors wish to thank him for his contributions. In particular, he has called our attention to the reverse martingale property of the empirical process together with the associated Birnbaum-Marshall inequality (cf.,the proofs of Lemmas 2.4 and 3.2) and to the Hardy inequality (cf. the proof of part (iv) of Theorem 4.1). These and several other related remarks helped us push down the 2 moment condition to EX
Kosorok’s brilliant text provides a self-contained introduction to empirical processes and semiparametric inference. These powerful research techniques are surprisingly useful for developing methods of statistical inference for complex models and in understanding the properties of such methods. This is an authoritative text that covers all the bases, and also a friendly and gradual introduction to the area. The book can be used as research reference and textbook.
It is an honor to be asked to write a foreword to this book, for I believe that it and other books to follow will eventually lead to a dramatic change in the current statistics curriculum in our universities. I spent the 1975-76 academic year at Florida State University in Tallahassee. My purpose was to complete a book on Statistical Reliability Theory with Frank Proschan. At the time, I was working on total time on test processes. At the same time, I started attending lectures by Dev Basu on statistical inference. It was Lehmann's hypothesis testing course and Lehmann's book was the text. However, I noticed something strange - Basu never opened the book. He was obviously not following it. Instead, he was giving a very elegant, measure theoretic treatment of the concepts of sufficiency, ancillarity, and invariance. He was interested in the concept of information - what it meant. - how it fitted in with contemporary statistics. As he looked at the fundamental ideas, the logic behind their use seemed to evaporate. I was shocked. I didn't like priors. I didn't like Bayesian statistics. But after the smoke had cleared, that was all that was left. Basu loves counterexamples. He is like an art critic in the field of statistical inference. He would find a counterexample to the Bayesian approach if he could. So far, he has failed in this respect.
"Prof. Nitis Mukhopadhyay and Prof. Partha Pratim Sengupta, who edited this volume with great attention and rigor, have certainly carried out noteworthy activities." - Giovanni Maria Giorgi, University of Rome (Sapienza) "This book is an important contribution to the development of indices of disparity and dissatisfaction in the age of globalization and social strife." - Shelemyahu Zacks, SUNY-Binghamton "It will not be an overstatement when I say that the famous income inequality index or wealth inequality index, which is most widely accepted across the globe is named after Corrado Gini (1984-1965). ... I take this opportunity to heartily applaud the two co-editors for spending their valuable time and energy in putting together a wonderful collection of papers written by the acclaimed researchers on selected topics of interest today. I am very impressed, and I believe so will be its readers." - K.V. Mardia, University of Leeds Gini coefficient or Gini index was originally defined as a standardized measure of statistical dispersion intended to understand an income distribution. It has evolved into quantifying inequity in all kinds of distributions of wealth, gender parity, access to education and health services, environmental policies, and numerous other attributes of importance. Gini Inequality Index: Methods and Applications features original high-quality peer-reviewed chapters prepared by internationally acclaimed researchers. They provide innovative methodologies whether quantitative or qualitative, covering welfare economics, development economics, optimization/non-optimization, econometrics, air quality, statistical learning, inference, sample size determination, big data science, and some heuristics. Never before has such a wide dimension of leading research inspired by Gini's works and their applicability been collected in one edited volume. The volume also showcases modern approaches to the research of a number of very talented and upcoming younger contributors and collaborators. This feature will give readers a window with a distinct view of what emerging research in this field may entail in the near future.
The book deals with bilinear forms in real random vectors and their generalizations as well as zonal polynomials and their applications in handling generalized quadratic and bilinear forms. The book is mostly self-contained. It starts from basic principles and brings the readers to the current research level in these areas. It is developed with detailed proofs and illustrative examples for easy readability and self-study. Several exercises are proposed at the end of the chapters. The complicated topic of zonal polynomials is explained in detail in this book. The book concentrates on the theoretical developments in all the topics covered. Some applications are pointed out but no detailed application to any particular field is attempted. This book can be used as a textbook for a one-semester graduate course on quadratic and bilinear forms and/or on zonal polynomials. It is hoped that this book will be a valuable reference source for graduate students and research workers in the areas of mathematical statistics, quadratic and bilinear forms and their generalizations, zonal polynomials, invariant polynomials and related topics, and will benefit statisticians, mathematicians and other theoretical and applied scientists who use any of the above topics in their areas. Chapter 1 gives the preliminaries needed in later chapters, including some Jacobians of matrix transformations. Chapter 2 is devoted to bilinear forms in Gaussian real ran dom vectors, their properties, and techniques specially developed to deal with bilinear forms where the standard methods for handling quadratic forms become complicated.
The aim of this book is to discuss various aspects associated with disseminating personal or business data collected in censuses or surveys or copied from administrative sources. The problem is to present the data in such a form that they are useful for statistical research and to provide sufficient protection for the individuals or businesses to whom the data refer. The major part of this book is concerned with how to define the disclosure problem and how to deal with it in practical circumstances.
In the last decade, graphical models have become increasingly popular as a statistical tool. This book is the first which provides an account of graphical models for multivariate complex normal distributions. Beginning with an introduction to the multivariate complex normal distribution, the authors develop the marginal and conditional distributions of random vectors and matrices. Then they introduce complex MANOVA models and parameter estimation and hypothesis testing for these models. After introducing undirected graphs, they then develop the theory of complex normal graphical models including the maximum likelihood estimation of the concentration matrix and hypothesis testing of conditional independence.