Asymptotic Theory of Statistics and Probability

This unique book delivers an encyclopedic treatment of classic as well as contemporary large sample theory. It deals with both statistical problems and probabilistic issues and tools. The book's detailed coverage is written in an extremely lucid style.

This unique book provides unmatched coverage of topics of interest to a very broad spectrum of statisticians and also probabilists. The book can be used in multiple roles. It can be used as a graduate text with a huge choice of topics for the instructor, as an invaluable general purpose reference, for independent reading by students and researchers, and for getting an overview of the latest developments in some of the most contemporary topics, such as false discovery, treatment of dependent data, and the bootstrap. There is no other book in large sample theory that matches this book in coverage, exercises and examples, bibliography, and lucid conceptual discussion of issues and theorems.

Encyclopedic coverage of classical topics and at the same time of some of the most modern topics Versatile research reference to anyone working on theoretical statistics and probability Emphasis on presenting the material in a lucid and accessible style, suitable for conceptual understanding of a very broad range of topics Includes supplementary material: sn.pub/extras

Autorentext

Anirban DasGupta has been professor of statistics at Purdue University since 1994. He is the author of Springer's Asymptotic Theory of Probability and Statistics, and Fundamentals of Probability, A First Course. He is an associate editor of the Annals of Statistics and has also served on the editorial boards of JASA, Journal of Statistical Planning and Inference, International Statistical Review, Statistics Surveys, Sankhya, and Metrika. He has edited four research monographs, and has recently edited the selected works of Debabrata Basu. He was elected a Fellow of the IMS in 1993, is a former member of the IMS Council, and has authored a total of 105 monographs and research articles.

Inhalt
Basic Convergence Concepts and Theorems.- Metrics, Information Theory, Convergence, and Poisson Approximations.- More General Weak and Strong Laws and the Delta Theorem.- Transformations.- More General Central Limit Theorems.- Moment Convergence and Uniform Integrability.- Sample Percentiles and Order Statistics.- Sample Extremes.- Central Limit Theorems for Dependent Sequences.- Central Limit Theorem for Markov Chains.- Accuracy of Central Limit Theorems.- Invariance Principles.- Edgeworth Expansions and Cumulants.- Saddlepoint Approximations.- U-statistics.- Maximum Likelihood Estimates.- M Estimates.- The Trimmed Mean.- Multivariate Location Parameter and Multivariate Medians.- Bayes Procedures and Posterior Distributions.- Testing Problems.- Asymptotic Efficiency in Testing.- Some General Large-Deviation Results.- Classical Nonparametrics.- Two-Sample Problems.- Goodness of Fit.- Chi-square Tests for Goodness of Fit.- Goodness of Fit with Estimated Parameters.- The Bootstrap.- Jackknife.- Permutation Tests.- Density Estimation.- Mixture Models and Nonparametric Deconvolution.- High-Dimensional Inference and False Discovery.- A Collection of Inequalities in Probability, Linear Algebra, and Analysis.