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Empirical Processes with Applications to Statistics

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By Galen R. Shorack and Jon A. Wellner


2009 / xlii + 956 pages / Softcover / ISBN: 978-0898716-84-9 / List Price $101.00 / SIAM Member Price $70.70 / Order Code CL59

Keywords: limit theorems in statistics, empirical process

Originally published in 1986, this valuable reference provides

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

This book is appropriate for researchers in statistical theory, probability theory, biostatistics, econometrics, and computer science.

Preface for Classics Edition;
Chapter 1: Introduction and Survey of Results;
Chapter 2: Foundations, Special Spaces and Special Processes;
Chapter 3: Convergence and Distributions of Empirical Processes;
Chapter 4: Alternatives and Processes of Residuals;
Chapter 5: Integral Test of Fit and Estimated Empirical Process;
Chapter 6: Martingale Methods;
Chapter 7: Censored data; the Product-Limit Estimator;
Chapter 8: Poisson and Exponential Representations;
Chapter 9: Some Exact Distributions;
Chapter 10: Linear and Nearly Linear Bounds on the Empirical Distribution Function Gn;
Chapter 11: Exponential Inequalities and ║∙/q║ -Metric Convergence of Un and Vn;
Chapter 12: The Hungarian Constructions of Kn, Un, and Vn;
Chapter 13: Laws of the Iterated Logarithm Associated with Un and Vn;
Chapter 14: Oscillations of the Empirical Process;
Chapter 15: The Uniforma Empirical Difference Process Dn≡Un + Vn;
Chapter 16: The Normalized Uniform Empirical Process Zn and the Normalized Uniform Quantile Process;
Chapter 17: The Uniform Empirical Process Indexed by Intervals and Functions;
Chapter 18: The Standardized Quantile Process Qn;
Chapter 19: L-Statistics;
Chapter 20: Rank Statistics;
Chapter 21: Spacing;
Chapter 22: Symmetry;
Chapter 23: Further Applications;
Chapter 24: Large Deviations;
Chapter 25: Independent but not Identically Distributed Random Variable;
Chapter 26: Empirical Measures and Processes for General Spaces;
Appendix A: Inequalities and Miscellaneous;
Appendix B: Counting Processes Martingales;
Author Index;
Subject Index.

About the Authors
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.

Jon A. Wellner is a Professor of Statistics at the University of Washington. He is a Fellow of the Institute of Mathematical Statistics, the American Statistical Association, and the American Association for the Advancement of Science. He has written three other books on probability and statistics.

ISBN: 9780898716849

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