Weak Convergence and Empirical Processes: With Applications to Statistics (Springer Series in Statistics)

( This book explores weak convergence theory and empirica...)

This book explores weak convergence theory and empirical processes and their applications to many applications in statistics. Part one reviews stochastic convergence in its various forms. Part two offers the theory of empirical processes in a form accessible to statisticians and probabilists. Part three covers a range of topics demonstrating the applicability of the theory to key questions such as measures of goodness of fit and the bootstrap.

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Efficient and Adaptive Estimation for Semiparametric Models (Johns Hopkins Studies in the Mathematical Sciences)

(Wherever statistics is applied, the need to combine inter...)

Wherever statistics is applied, the need to combine interpretable structure with a minimum of assumptions about random fluctuations leads to the use of semiparametric models. In theories of economic choice, for instance, decision making is modeled in part by parametric relations suggested by economic theory and in part by individual fluctuations about which little is known or assumed. Another well-known example, the proportional hazards model of survival analysis, permits an arbitrary baseline hazard rate for a human lifetime but postulates that such variables as medical treatment, age and gender act on the baseline only through parametric scaling factors. This book unifies the theory of estimation in such examples. The authors show how the classical information bounds developed for parametric models extend naturally to nonparametric and semiparametric models. They then apply these techniques in as broad a range of models as possible, illustrating the ease with which heuristic calculations of "optimal behaviour" can be carried out.

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Weak Convergence and Empirical Processes: With Applications to Statistics (Springer Series in Statistics) by A.W. van der vaart (2000-11-10)

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Empirical Processes With Applications to Statistics (Classics in Applied Mathematics)

(Originally published in 1986, this valuable reference pro...)

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

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Efficient and Adaptive Estimation for Semiparametric Models (1384)

(This book deals with estimation in situations in which th...)

This book deals with estimation in situations in which there is believed to be enough information to model parametrically some, but not all of the features of a data set. Such models have arisen in a wide context in recent years, and involve new nonlinear estimation procedures. Statistical models of this type are directly applicable to fields such as economics, epidemiology, and astronomy.

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