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.
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"...an up-to-date and comprehensive account of the title theme...provides a path to several major research frontiers in the bootstrap literature." - Journal of the American Statistical Association
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25 of 26 people found the following review helpful:
5.0 out of 5 stars
excellent treatment of asymptotic theory through Edgeworth and other expansions,
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This review is from: The Bootstrap and Edgeworth Expansion (Springer Series in Statistics) (Paperback)
I wrote a book on bootstrap methods at the same time that Peter Hall was writing his. He kindly sent me an advance copy of the manuscript. This enabled me to incorporate some very useful information in my book. The material is advanced and rigorous. However the asymptotic results for Edgeworth and Cornish-Fisher expansions provide important insight into the advantages of bootstrap and the special modifications such as bootstrap iteration and various other bootstrap variants for confidence intervals including Efron's BCa method. It is well written but requires a good mathematical background and knowledge of advanced probability would be helpful. It is not easy reading even for Ph.D students and postdoctoral researchers but is certainly worth the effort.
0 of 1 people found the following review helpful:
4.0 out of 5 stars
Theory of bootstrap,
This review is from: The Bootstrap and Edgeworth Expansion (Springer Series in Statistics) (Paperback)
This book is a great reference for the theory of bootstrap. However, it lacks applications, so practicioners should look for other references.
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Inside This Book
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First Sentence:
The idea behind the bootstrap is an old one. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
other percentile method, perfect coverage accuracy, explicit regularity conditions, last identity following, nonpivotal statistic, separable arrays, smooth function model, accelerated bias correction, symmetric bootstrap confidence intervals, symmetry conferred, resampling approximation, bootstrap iteration, resampling principle, replacing population moments, multivariate confidence regions, cumulant sequence, jth cumulant, coverage error, multiparameter regression, bootstrap confidence bands, short confidence intervals, skewness correction, iterated bootstrap, pivotal methods, bootstrap hypothesis testing Key Phrases - Capitalized Phrases (CAPs): (learn more)
Standard Normal, Monte Carlo, Edgeworth Expansions of Coverage Probability New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The idea behind the bootstrap is an old one. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
other percentile method, perfect coverage accuracy, explicit regularity conditions, last identity following, nonpivotal statistic, separable arrays, smooth function model, accelerated bias correction, symmetric bootstrap confidence intervals, symmetry conferred, resampling approximation, bootstrap iteration, resampling principle, replacing population moments, multivariate confidence regions, cumulant sequence, jth cumulant, coverage error, multiparameter regression, bootstrap confidence bands, short confidence intervals, skewness correction, iterated bootstrap, pivotal methods, bootstrap hypothesis testing Key Phrases - Capitalized Phrases (CAPs): (learn more)
Standard Normal, Monte Carlo, Edgeworth Expansions of Coverage Probability New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 75
books:
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100
books
cite this book:
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- Markov Chains (Cambridge Series in Statistical and Probabilistic Mathematics) by J. R. Norris in Front Matter, and Back Matter
- Statistical Decision Theory: Foundations, Concepts, and Methods (Springer Series in Statistics) by J.O. Berger in Front Matter, and Back Matter
- New Perspectives in Theoretical and Applied Statistics by Madan Lal Puri in Back Matter (1), and Back Matter (2)
- Regeneration and Networks of Queues (Applied Probability) (v. 3) by Gerald S. Shedler in Back Matter
- Bayes Theory (Springer Series in Statistics) by J. A. Hartigan in Front Matter
See all 75 books this book cites
- Simulation-based Inference in Econometrics: Methods and Applications by Roberto Mariano on page 357, and page 456
- Applied Regression Analysis (Wiley Series in Probability and Statistics) by Norman R. Draper on page 588, and Back Matter
- An Introduction to the Bootstrap (Chapman & Hall/CRC Monographs on Statistics & Applied Probability) by Bradley Efron on page 8, and Back Matter
- Numerical Analysis for Statisticians by Kenneth Lange on page 234, and page 312
- Nonparametric Smoothing and Lack-of-Fit Tests (Springer Series in Statistics) by Jeffrey Hart in Front Matter, and Back Matter
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