Probability and Its Applications

Decoupling

From Dependence to Independence

Authors: Peña, Victor de la, Giné, Evarist

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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

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MATHEMATICAL REVIEWS

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


Table of contents (8 chapters)

  • Sums of Independent Random Variables

    Peña, Víctor H. (et al.)

    Pages 1-50

  • Randomly Stopped Processes with Independent Increments

    Peña, Víctor H. (et al.)

    Pages 51-95

  • Decoupling of U-Statistics and U-Processes

    Peña, Víctor H. (et al.)

    Pages 97-152

  • Limit Theorems for U-Statistics

    Peña, Víctor H. (et al.)

    Pages 153-206

  • Limit Theorems for U -rocesses

    Peña, Víctor H. (et al.)

    Pages 207-290

Buy this book

eBook $129.00
price for USA in USD (gross)
  • ISBN 978-1-4612-0537-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.99
price for USA in USD
  • ISBN 978-0-387-98616-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $169.99
price for USA in USD
  • ISBN 978-1-4612-6808-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Decoupling
Book Subtitle
From Dependence to Independence
Authors
Series Title
Probability and Its Applications
Copyright
1999
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-0537-1
DOI
10.1007/978-1-4612-0537-1
Hardcover ISBN
978-0-387-98616-6
Softcover ISBN
978-1-4612-6808-6
Series ISSN
1431-7028
Edition Number
1
Number of Pages
XV, 392
Topics