Decoupling: From Dependence to Independence (Probability and Its Applications) - Hardcover

Peña, Victor De La; Giné, Evarist

Hardcover

ISBN 10: 0387986162 ISBN 13: 9780387986166

Publisher: Springer, 1998

Synopsis

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

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Review

From a review:

MATHEMATICAL REVIEWS

"The book is written in an excellent way. The exposition is clear and effective. The results are well motivated."

Synopsis

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, moment 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 exposition 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 Pena is Associate Professor of Statistics at Columbia University and is one of the more active developers of decoupling.

Edition details

• Publisher: Springer
• Publication date: 1998
• Language: English
• ISBN 10: 0387986162
• ISBN 13: 9780387986166
• Binding: Hardcover
• Number of pages: 407