Empirical Processes with Applications to Statistics

Häftad, Engelska, 2009

Av Galen R. Shorack, Jon A. Wellner, Galen R Shorack, Jon A Wellner

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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.

Produktinformation

Utgivningsdatum2009-09-30
Mått152 x 229 x 48 mm
Vikt1 353 g
FormatHäftad
SpråkEngelska
SerieClassics in Applied Mathematics
Antal sidor997
FörlagSociety for Industrial & Applied Mathematics,U.S.
ISBN9780898716849

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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.

Preface to Classics EditionPrefaceList of TablesList of Special SymbolsChapter 1: Introduction and Survey of ResultsChapter 2: Foundations, Special Spaces and Special ProcessesChapter 3: Convergence and Distributions of Empirical ProcessesChapter 4: Alternatives and Processes of ResidualsChapter 5: Integral Test of Fit and Estimated Empirical ProcessChapter 6: Martingale MethodsChapter 7: Censored datathe Product-Limit EstimatorChapter 8: Poisson and Exponential RepresentationsChapter 9: Some Exact DistributionsChapter 10: Linear and Nearly Linear Bounds on the Empirical Distribution Function GnChapter 11: Exponential Inequalities and ??/q? -Metric Convergence of Un and VnChapter 12: The Hungarian Constructions of Kn, Un, and VnChapter 13: Laws of the Iterated Logarithm Associated with Un and VnChapter 14: Oscillations of the Empirical ProcessChapter 15: The Uniforma Empirical Difference Process Dn?Un + VnChapter 16: The Normalized Uniform Empirical Process Zn and the Normalized Uniform Quantile ProcessChapter 17: The Uniform Empirical Process Indexed by Intervals and FunctionsChapter 18: The Standardized Quantile Process QnChapter 19: L-StatisticsChapter 20: Rank StatisticsChapter 21: SpacingChapter 22: SymmetryChapter 23: Further ApplicationsChapter 24: Large DeviationsChapter 25: Independent but not Identically Distributed Random VariableChapter 26: Empirical Measures and Processes for General SpacesAppendix A: Inequalities and MiscellaneousAppendix B: Counting Processes MartingalesErrataReferencesAuthor IndexSubject Index