The bootstrap and Edgeworth expansion
著者
書誌事項
The bootstrap and Edgeworth expansion
（Springer series in statistics）
Springer-Verlag, c1992
- : us
- : gw
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注記
Includes bibliographical references (p. 329-344) and indexes
内容説明・目次
- 巻冊次
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: us ISBN 9780387977201
内容説明
This monograph addresses two quite different topics, each being able to shed light on the other. Firstly, it lays the foundation for a particular view of the bootstrap. Secondly, it gives an account of Edgeworth expansion. The first two chapters deal with the bootstrap and Edgeworth expansion respectively, while chapters 3 and 4 bring these two themes together, using Edgeworth expansion to explore and develop the properties of the bootstrap. The book is aimed at graduate level for those with some exposure to the methods of theoretical statistics. However, technical details are delayed until the last chapter such that mathematically able readers without knowledge of the rigorous theory of probability will have no trouble understanding most of the book.
目次
1: Principles of Bootstrap Methodology.- 2: Principles of Edgeworth Expansion.- 3: An Edgeworth View of the Bootstrap.- 4: Bootstrap Curve Estimation.- 5: Details of Mathematical Rigour.- Appendix I: Number and Sizes of Atoms of Nonparametric Bootstrap Distribution.- Appendix II: Monte Carlo Simulation.- II.1 Introduction.- II.2 Uniform Resampling.- II.3 Linear Approximation.- II.4 Centring Method.- II.5 Balanced Resampling.- II.6 Antithetic Resampling.- II.7 Importance Resampling.- II.7.1 Introduction.- II.7.2 Concept of Importance Resampling.- II.7.3 Importance Resampling for Approximating Bias, Variance, Skewness, etc..- II.7.4 Importance Resampling for a Distribution Function.- II.8 Quantile Estimation.- Appendix III: Confidence Pictures.- Appendix IV: A Non-Standard Example: Quantite Error Estimation.- IV. 1 Introduction.- IV.2 Definition of the Mean Squared Error Estimate.- IV.3 Convergence Rate of the Mean Squared Error Estimate.- IV.4 Edgeworth Expansions for the Studentized Bootstrap Quantile Estimate.- Appendix V: A Non-Edgeworth View of the Bootstrap.- References.- Author Index.
- 巻冊次
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: gw ISBN 9783540977209
内容説明
The aim of this book is to present a readable introduction to the theory of bootstrap methods which is suitable for graduate students and research workers in statistics. In particular, the author discusses the application of bootstrap methods to linear regression, non-parametric regression and density estimation. The author's perspective is that the Edgeworth expansion sheds important light on the performance of bootstrap methods and that, conversely, bootstrap methods motivate a renewed interest in the study of the Edgeworth expansion. Consequently, the book is structured to first present chapters which introduce the basic concepts of bootstrap methods and the Edgeworth expansion. Subsequent chapters then explore the interaction between the two subjects and their application to statistical techniques. Generally, technical details are deferred to the last chapter so as to enable a reader with a relatively small exposure to theoretical statistics to enjoy this account of a rapidly growing branch of statistical research.
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