Synopses & Reviews
A friendly and systematic introduction to the theory and applications. The book begins with the 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 to randomly stopped processes and unbiased estimation. The authors then proceed with the theory of decoupling in full generality, paying special attention to comparison and interplay between martingale and decoupling theory, and to applications. These include limit theorems, moment and exponential inequalities for martingales and more general dependence structures, biostatistical implications, and moment convergence in Anscombe's theorem and Wald's equation for U--statistics. Addressed to researchers in probability and statistics and to graduates, 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.
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
This friendly and systematic introduction to the theory and applications of decoupling gives special attention to the comparison and interplay between martingale and decoupling theory, and also considers applications.
Table of Contents
Sums of Independent Random Variables.- Randomly Stopped Processes with Independent Increments.- Decoupling of U-Statistics and U-Processes.- Limit Theorems for U-Statistics.- Limit Theorems for Degenerate U-Processes.- General Decoupling Inequalities for Tangent Sequences.- Conditionally Independent Sequences.- Further Applications of Decoupling.