Empirical Processes with Applications to Statistics
Empirical Processes with Applications to Statistics
September 2009
Paperback
9780898716849
Paperback
Originally published in 1986, this valuable reference provides a detailed treatment of limit theorems and inequalities for empirical processes of real-valued random variables. It also includes applications of the theory to censored data, spacings, rank statistics, quantiles, and many functionals of empirical processes, including a treatment of bootstrap methods, and a summary of inequalities that are useful for proving limit theorems. At the end of the Errata section, the authors have supplied references to solutions for 11 of the 19 Open Questions provided in the book's original edition.
- A classic originally published in 1986
- A valuable resource for researchers in statistical theory, probability theory, biostatistics, econometrics and computer science
- Contains a solid treatment of Martingale approaches to right-censored data
Product details
September 2009Paperback
9780898716849
948 pages
230 × 150 × 48 mm
1.34kg
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Table of Contents
- Preface for Classics Edition
- Preface
- 1. Introduction and survey of results
- 2. Foundations, special spaces and special processes
- 3. Convergence and distributions of empirical processes
- 4. Alternatives and processes of residuals
- 5. Integral test of fit and estimated empirical process
- 6. Martingale methods
- 7. Censored data: the product-limit estimator
- 8. Poisson and exponential representations
- 9. Some exact distributions
- 10. Linear and nearly linear bounds on the empirical distribution function Gn
- 11. Exponential inequalities and ║∙/q║ -metric convergence of Un and Vn
- 12. The Hungarian constructions of Kn, Un, and Vn
- 13. Laws of the iterated logarithm associated with Un and Vn
- 14. Oscillations of the empirical process
- 15. The uniform empirical difference process Dn≡Un + Vn
- 16. The normalized uniform empirical process Zn and the normalized uniform quantile process
- 17. The uniform empirical process indexed by intervals and functions
- 18. The standardized quantile process Qn
- 19. L-statistics
- 20. Rank statistics
- 21. Spacing
- 22. Symmetry
- 23. Further applications
- 24. Large deviations
- 25. Independent but not identically distributed random variable
- 26. Empirical measures and processes for general spaces
- Appendix A. Inequalities and miscellaneous
- Appendix B. Counting processes Martingales
- References
- Errata
- Author index
- Subject index.
