This book developed out of my year-long course on asymptotic theory at Purdue University. To some extent, the topics coincide with what I cover in that course. There are already a number of well-known books on asy- totics. This book is quite different. It covers more topics in one source than areavailableinanyothersinglebookonasymptotictheory. Numeroustopics covered in this book are available in the literature in a scattered manner, and they are brought together under one umbrella in this book. Asymptotic theory is a central unifying theme in probability and statistics. My main goal in writing this book is to give its readers a feel for the incredible scope and reach of asymptotics. I have tried to write this book in a way that is accessible and to make the reader appreciate the beauty of theory and the insights that only theory can provide. Essentially every theorem in the book comes with at least one reference, preceding or following the statement of the theorem. In addition, I have p- vided a separate theorem-by-theorem reference as an entry on its own in the front of the book to make it extremely convenient for the reader to ?nd a proof that was not provided in the text. Also particularly worth mentioning is a collection of nearly 300 practically useful inequalities that I have c- lected together from numerous sources. This is appended at the very end of the book.
This book is an encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. It is written in an extremely lucid style, with an emphasis on the conceptual discussion of the importance of a problem and the impact and relevance of the theorems. The book has 34 chapters over a wide range of topics, nearly 600 exercises for practice and instruction, and another 300 worked out examples. It also includes a large compendium of 300 useful inequalities on probability, linear algebra, and analysis that are collected together from numerous sources, as an invaluable reference for researchers in statistics, probability, and mathematics.
It can be used as a graduate text, as a versatile research reference, as a source for independent reading on a wide assembly of topics, and as a window to learning the latest developments in contemporary topics. The book is unique in its detailed coverage of fundamental topics such as central limit theorems in numerous setups, likelihood based methods, goodness of fit, higher order asymptotics, as well as of the most modern topics such as the bootstrap, dependent data, Bayesian asymptotics, nonparametric density estimation, mixture models, and multiple testing and false discovery. It provides extensive bibliographic references on all topics that include very recent publications.
Anirban DasGupta is Professor of Statistics at Purdue University. He has also taught at the Wharton School of the University of Pennsylvania, at Cornell University, and at the University of California at San Diego. He has been on the editorial board of the Annals of Statistics since 1998 and has also served on the editorial boards of the Journal of the American Statistical Association, International Statistical Review, and the Journal of Statistical Planning and Inference. He has edited two monographs in the lecture notes monograph series of the Institute of Mathematical Statistics, is a Fellow of the Institute of Mathematical Statistics and has 70 refereed publications on theoretical statistics and probability in major journals.
