Limit Theory for Mixing Dependent Random Variables / Edition 1

Limit Theory for Mixing Dependent Random Variables / Edition 1

by Lin Zhengyan, Lu Chuanrong, Zhengyan Lin Zhengyan
     
 

ISBN-10: 0792342194

ISBN-13: 9780792342199

Pub. Date: 07/31/1997

Publisher: Springer Netherlands

For many practical problems, observations are not independent. In this book, limit behaviour of an important kind of dependent random variables, the so-called mixing random variables, is studied. Many profound results are given, which cover recent developments in this subject, such as basic properties of mixing variables, powerful probability and moment

Overview

For many practical problems, observations are not independent. In this book, limit behaviour of an important kind of dependent random variables, the so-called mixing random variables, is studied. Many profound results are given, which cover recent developments in this subject, such as basic properties of mixing variables, powerful probability and moment inequalities, weak convergence and strong convergence (approximation), limit behaviour of some statistics with a mixing sample, and many useful tools are provided.
Audience: This volume will be of interest to researchers and graduate students in the field of probability and statistics, whose work involves dependent data (variables).

Product Details

ISBN-13:
9780792342199
Publisher:
Springer Netherlands
Publication date:
07/31/1997
Series:
Mathematics and Its Applications (closed) Series, #378
Edition description:
1996
Pages:
430
Product dimensions:
1.06(w) x 6.14(h) x 9.21(d)

Table of Contents

Preface. Part I: Introduction. 1. Definitions and Basic Inequalities. 2. Moment Estimations of Partial Sums. Part II: Weak Convergence. 3. Weak Convergence for alpha-Mixing Sequences. 4. Weak Convergence for rho-Mixing Sequences. 5. Weak Convergence for phi-Mixing Sequences. 6. Weak Convergence for Mixing Random Fields. 7. The Berry-Esseen Inequality and the Rate of Weak Convergence. Part III: Almost Sure Convergence and Strong Approximations. 8. Laws of Large Numbers and Complete Convergence. 9. Strong Approximations. 10. The Increments of Partial Sums. 11. Strong Approximations for Mixing Random Fields. Part IV: Statistics of a Dependent Sample. 12. Empirical Processes. 13. Convergence of Some Statistics with a Mixing Sample. 14. Strong Approximations for Other Kinds of Dependent Random Variables. Appendix. References. Index.

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