Buch, Englisch, Band 378, 430 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1770 g
Buch, Englisch, Band 378, 430 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1770 g
Reihe: Mathematics and Its Applications
ISBN: 978-0-7923-4219-9
Verlag: 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 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).
Zielgruppe
Research
Fachgebiete
- Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
- Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung
- Mathematik | Informatik Mathematik Stochastik Elementare Stochastik
- Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
- Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
Weitere Infos & Material
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.
