Overview
- Authors:
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Víctor H. Peña
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Department of Statistics, Columbia University, New York, USA
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Evarist Giné
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Department of Mathematics, University of Connecticut, Storrs, Storrs, USA
- A friendly and systematic introduction to the theory and applications of decoupling Special emphasis is given to the comparison and interplay between martingale and decoupling theories Applications are emphasized and include results with biostatistical implications Authors are recognized experts in this area
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Table of contents (8 chapters)
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- Víctor H. de la Peña, Evarist Giné
Pages 1-50
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- Víctor H. de la Peña, Evarist Giné
Pages 51-95
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- Víctor H. de la Peña, Evarist Giné
Pages 97-152
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- Víctor H. de la Peña, Evarist Giné
Pages 153-206
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- Víctor H. de la Peña, Evarist Giné
Pages 207-290
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- Víctor H. de la Peña, Evarist Giné
Pages 291-324
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- Víctor H. de la Peña, Evarist Giné
Pages 325-348
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- Víctor H. de la Peña, Evarist Giné
Pages 349-375
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Back Matter
Pages 377-392
About this book
Decoupling theory provides a general framework for analyzing problems involving dependent random variables as if they were independent. It was born in the early eighties as a natural continuation of martingale theory and has acquired a life of its own due to vigorous development and wide applicability. The authors provide a friendly and systematic introduction to the theory and applications of decoupling. The book begins with a chapter on sums of independent random variables and vectors, with maximal inequalities and sharp estimates on moments which are later used to develop and interpret decoupling inequalities. Decoupling is first introduced as it applies in two specific areas, randomly stopped processes (boundary crossing problems) and unbiased estimation (U-- statistics and U--processes), where it has become a basic tool in obtaining several definitive results. In particular, decoupling is an essential component in the development of the asymptotic theory of U-- statistics and U--processes. The authors then proceed with the theory of decoupling in full generality. Special attention is given to comparison and interplay between martingale and decoupling theory, and to applications. Among other results, the applications include limit theorems, momemt and exponential inequalities for martingales and more general dependence structures, results with biostatistical implications, and moment convergence in Anscombe's theorem and Wald's equation for U--statistics. This book is addressed to researchers in probability and statistics and to graduate students. The expositon is at the level of a second graduate probability course, with a good portion of the material fit for use in a first year course. Victor de la Pe$a is Associate Professor of Statistics at Columbia University and is one of the more active developers of decoupling
Reviews
From a review:
MATHEMATICAL REVIEWS
"The book is written in an excellent way. The exposition is clear and effective. The results are well motivated."
Authors and Affiliations
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Department of Statistics, Columbia University, New York, USA
Víctor H. Peña
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Department of Mathematics, University of Connecticut, Storrs, Storrs, USA
Evarist Giné