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 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 tools are provided. This book should be of interest to researchers and graduate students in the field of probability and statistics, whose work involves dependent data (variables).

Full Product Details

Author:   Lin Zhengyan ,  Lu Chuanrong
Publisher:   Springer
Imprint:   Springer
Edition:   1996 ed.
Volume:   378
Dimensions:   Width: 15.60cm , Height: 2.50cm , Length: 23.40cm
Weight:   1.770kg
ISBN:  

9780792342199

ISBN 10:   0792342194
Pages:   430
Publication Date:   31 July 1997
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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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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