Robust asymptotic statistics
著者
書誌事項
Robust asymptotic statistics
（Springer series in statistics）
Springer-Verlag, c1994
- : us
- : gw
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注記
Includes bibliographical references and index
内容説明・目次
- 巻冊次
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: us ISBN 9780387942629
内容説明
1 To the king, my lord, from your servant Balasi: 2 ... The king should have a look. Maybe the scribe who reads to the king did not understand . . . . shall I personally show, with this tablet that I am sending to the king, my lord, how the omen was written. 3 Really, he who has not followed the text with his finger cannot possibly understand it. This book is about optimally robust functionals and their unbiased esti mators and tests. Functionals extend the parameter of the assumed ideal center model to neighborhoods of this model that contain the actual distri bution. The two principal questions are (F): Which functional to choose? and (P): Which statistical procedure to use for the selected functional? Using a local asymptotic framework, we deal with both problems by linking up nonparametric statistical optimality with infinitesimal robust ness criteria. Thus, seemingly separate developments in robust statistics are presented in a unifying way."
- 巻冊次
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: gw ISBN 9783540942627
内容説明
This volume gives a rigorous account of the asymptotic theory of robust statistics, from the viewpoint of optimally robust functionals and their unbiased estimators and tests. By linking up the local asymptotic minimax criterion with further optimality, the author creates a powerful and unifying notion of robustness. Consequently, this volume gives a self-contained treatment of the main optimality results of asymptotic statistics, and supplies the necessary tools of convex optimization and weak convergence. The volume is an ideal reference for researchers who work in statistics and graduate students with a basic knowledge of probability and statistics. Some of the main topics covered are von Mises functionals, log-likelihoods, asymptotic statistics, nonparametric statistics, optimal influence curves, the constructional problem, and robust regression.
目次
Contents: Preface.- Notation.- Chapter 1: Von Mises Functionals.- Chapter 2: Log Likelihoods.- Chapter 3: Asymptotic Statistics.- Chapter 4: Nonparametric Statistics.- Chapter 5: Optimal Influence Curves.- Chapter 6: Stable Constructions.- Chapter 7: Robust Regression.- Appendix A: Weak Convergence of Measures.- Appendix B: Some Functional Analysis.- Appendix C: Complements.- Bibliography.- Index.
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