Lin Zhengyan, Lu Chuanrong

Limit Theory for Mixing Dependent Random Variables

• Broschiertes Buch

Produktbeschreibung

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).

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Produktdetails

• Mathematics and Its Applications 378
• Verlag: Science Press / Springer / Springer Netherlands
• Artikelnr. des Verlages: 978-90-481-4748-9
• Softcover reprint of hardcover 1st ed. 1996
• Seitenzahl: 444
• Erscheinungstermin: 9. Dezember 2010
• Englisch
• Abmessung: 235mm x 155mm x 24mm
• Gewicht: 668g
• ISBN-13: 9789048147489
• ISBN-10: 9048147484
• Artikelnr.: 32094205

Inhaltsangabe

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.