Decoupling
Subtitle: From Dependence to Independence
By: by Víctor H. Peña, Evarist Giné
Contributors: Giné, Evarist
Series: Probability and its Applications, A Series of the Applied Probability Trust; Probability and its Applications, A Series of the Applied Probability Trust
Publisher: Springer New York
Published: 1999
Place of publication: New York, NY
Language: eng
Format: [electronic resource] :
Number of pages: 392
ISBN-13: 9781461268086; 9781461205371
Subjects: Mathematics; Distribution (Probability theory); Statistics
Other titles: Randomly Stopped Processes U-Statistics and Processes Martingales and Beyond
Description: 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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Table of contents: title: Sums of Independent Random Variables; title: Randomly Stopped Processes with Independent Increments; title: Decoupling of U-Statistics and U-Processes; title: Limit Theorems for U-Statistics; title: Limit Theorems for Degenerate U-Processes; title: General Decoupling Inequalities for Tangent Sequences; title: Conditionally Independent Sequences; title: Further Applications of Decoupling.