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Limit Theory for Mixing Dependent Random Variables
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Artikel-Nr:
9780792342199
Veröffentl:
1997
Einband:
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Erscheinungsdatum:
31.07.1997
Seiten:
446
Autor:
Lu Chuanrong
Gewicht:
831 g
Format:
241x160x29 mm
Serie:
378, Mathematics and Its Applications
Sprache:
Englisch
Beschreibung:
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).
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).
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.