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Empirical Processes with Applications to Statistics: Classics in Applied Mathematics, cartea 59

Autor Galen R. Shorack, Jon A. Wellner
en Limba Engleză Paperback – 24 sep 2009
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.
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Specificații

ISBN-13: 9780898716849
ISBN-10: 0898716845
Pagini: 948
Dimensiuni: 174 x 247 x 48 mm
Greutate: 0 kg
Ediția:Revised
Editura: Society for Industrial and Applied Mathematics
Colecția Society for Industrial and Applied Mathematics
Seria Classics in Applied Mathematics

Locul publicării:Philadelphia, United States

Cuprins

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.

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Descriere

A detailed treatment of limit theorems and inequalities for empirical processes of real-valued random variables.