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基本説明
Originally published in 1986, this valuable reference provides a detailed treatment of limit theorems and inequalities for empirical processes of real-valued random variables.
Full Description
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.
Contents
Preface to Classics Edition
Preface
List of Tables
List of Special Symbols
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
Errata
References
Author Index
Subject Index
