Asymptotic Statistics

Cambridge Series in Statistical and Probabilistic Mathematics

by A.W. van der Vaart

This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications.

The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. setup with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way.

Suitable as a text for a graduate or Master's level statistics course, this book will also give researchers in statistics, probability, and their applications an overview of the latest research in asymptotic statistics.
--back cover

Genres: Textbooks, Mathematics

462 pages, Paperback

First published January 1, 1998

Reviews

[Victor]

recommended by Michael Jordan

[Zach Mackin · Rating 5 out of 5]

One of the more difficult textbooks I've ever read.

I read chapters 2, 3, 4, 5, 18, 19, 20, 24, and 25 which I felt were the main sections relevant to my research. Incredibly challenging, I think it is likely neccesary for any section to both read it a few times, work out everything, and have someone (e.g., a professor) who has read it many times before and can point you to what is important and what to take away.

vdV is absolutely brilliant and even difficult to understand for the most talented professors, so don't be discouraged in the struggle.

[Leonardo]

Del curso de Montes Rojas.

[Matthew Zhang · Rating 4 out of 5]

Great book but very challenging!