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Uniform central limit theorems
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ISBN: 9780521052214 9780521461023 0521461022 9780511665622 Year: 1999 Publisher: New York: Cambridge university press,

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Book
Uniform central limit theorems
Author:
ISBN: 0511665628 Year: 1999 Publisher: Cambridge : Cambridge University Press,

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Abstract

This book shows how the central limit theorem for independent, identically distributed random variables with values in general, multidimensional spaces, holds uniformly over some large classes of functions. The author, an acknowledged expert, gives a thorough treatment of the subject, including several topics not found in any previous book, such as the Fernique-Talagrand majorizing measure theorem for Gaussian processes, an extended treatment of Vapnik-Chervonenkis combinatorics, the Ossiander L2 bracketing central limit theorem, the Giné-Zinn bootstrap central limit theorem in probability, the Bronstein theorem on approximation of convex sets, and the Shor theorem on rates of convergence over lower layers. Other results of Talagrand and others are surveyed without proofs in separate sections. Problems are included at the end of each chapter so the book can be used as an advanced text. The book will interest mathematicians working in probability, mathematical statisticians and computer scientists working in computer learning theory.

Limit theorems for functionals of ergodic Markov chains with general state space
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ISSN: 00659266 ISBN: 082181060X Year: 1999 Publisher: Providence, R.I.

Elements of large-sample theory
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ISBN: 1280010428 9786610010424 0387227296 0387985956 9780387985954 Year: 1999 Publisher: New York (N.Y.): Springer,

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Elements of Large-Sample Theory provides a unified treatment of first- order large-sample theory. It discusses a broad range of applications including introductions to density estimation, the bootstrap, and the asymptotics of survey methodology. The book is written at an elementary level and is suitable for students at the master's level in statistics and in aplied fields who have a background of two years of calculus. E.L. Lehmann is Professor of Statistics Emeritus at the University of California, Berkeley. He is a member of the National Academy of Sciences and the American Academy of Arts and Sciences, and the recipient of honorary degrees from the University of Leiden, The Netherlands, and the University of Chicago. Also available: Lehmann/Casella, Theory at Point Estimation, 2nd ed. Springer-Verlag New York, Inc., 1998, ISBN 0- 387-98502-6 Lehmann, Testing Statistical Hypotheses, 2nd ed. Springer-Verlag New York, Inc., 1997, ISBN 0-387-94919-4.

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