Here is the first book to summarize a broad cross-section of the large volume of literature available on one-dimensional empirical processes. Presented is a thorough treatment of the theory of empirical processes, with emphasis on real random variable processes as well as a wide-ranging selection of applications in statistics. Featuring many tables and illustrations accompanying the proofs of major results, coverage includes foundations - special spaces and special processes, convergence and distribution of empirical processes, alternatives and processes of residuals, integral tests of fit and estimated empirical processes and martingale methods.
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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.
Galen R. Shorack is a Professor of Statistics at the University of Washington. He is a Fellow of the Institute of Mathematical Statistics and has written a graduate level text on probability theory.
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