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Decoupling

From Dependence to Independence

  • Víctor H. de la Peña
  • Evarist Giné

Part of the Probability and its Applications book series (PIA)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Víctor H. de la Peña, Evarist Giné
    Pages 1-50
  3. Víctor H. de la Peña, Evarist Giné
    Pages 51-95
  4. Víctor H. de la Peña, Evarist Giné
    Pages 97-152
  5. Víctor H. de la Peña, Evarist Giné
    Pages 153-206
  6. Víctor H. de la Peña, Evarist Giné
    Pages 207-290
  7. Víctor H. de la Peña, Evarist Giné
    Pages 291-324
  8. Víctor H. de la Peña, Evarist Giné
    Pages 325-348
  9. Víctor H. de la Peña, Evarist Giné
    Pages 349-375
  10. Back Matter
    Pages 377-392

About this book

Introduction

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

Keywords

Law of large numbers Martingale Maxima Random variable law of the iterated logarithm random function statistics

Authors and affiliations

  • Víctor H. de la Peña
    • 1
  • Evarist Giné
    • 2
  1. 1.Department of StatisticsColumbia UniversityNew YorkUSA
  2. 2.Department of MathematicsUniversity of Connecticut, StorrsStorrsUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0537-1
  • Copyright Information Springer-Verlag New York, Inc 1999
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6808-6
  • Online ISBN 978-1-4612-0537-1
  • Series Print ISSN 1431-7028
  • Buy this book on publisher's site
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