Here is a practical and mathematically rigorous introduction to the field of asymptotic statistics. In addition to most of the standard topics of an asymptotics course--likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures--the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, one of the book's unifying themes that mainly entails the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation.
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Book Description
Editorial Reviews
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'The book is extremely well written and clear ... it is comprehensive and has an abundant supply of worked examples ... anyone who is genuinely interested in learning about some of the recent developments in asymptotic statistics and their potential applications should have a copy of this book.' Biometrics
'I recommend this book to every advanced Master's student, Ph.D. student or researcher in mathematical statistics.' Kwantitatieve methoden
'I recommend this book to every advanced Master's student, Ph.D. student or researcher in mathematical statistics.' Kwantitatieve methoden
Book Description
This book is an introduction to the field of asymptotic statistics. The treatment is mathematically rigorous but practical rather than simply technical. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. In addition to the usual topics of an asymptotics course, the author also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes. Suitable as a text for a graduate or Master's level statistics course, this book will also serve as a reference for researchers in statistics, probability, and their applications.
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Most Helpful Customer Reviews
19 of 19 people found the following review helpful:
5.0 out of 5 stars
Excellent textbook on asymptotics in statistics,
By A Customer
This review is from: Asymptotic Statistics (Cambridge Series in Statistical and Probabilistic Mathematics) (Hardcover)
This book covers asymptotics at a level suitable for graduate students in statistics and other disciplines such as economics. It does not really treat time-series issues, but apart from that its coverage is very impressive. It covers M-estimators, efficiency, quantile estimators, semiparametrics, and much more. The writing is remarkably lucid; proofs are succinct but very readable. One feature I particularly liked was a very readable introduction to empirical process theory, which would be a good place to start before tackling the van der Vaart and Wellner's more advanced book.
1 of 8 people found the following review helpful:
5.0 out of 5 stars
Just read and enjoy.,
This review is from: Asymptotic Statistics (Cambridge Series in Statistical and Probabilistic Mathematics) (Paperback)
An excellent book for graduate level. Many interesting material (like U-statistics and a flavor of nonparametric methods) exposed in a solid and precise way.
0 of 9 people found the following review helpful:
5.0 out of 5 stars
Asymptotic Statistics,
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This review is from: Asymptotic Statistics (Cambridge Series in Statistical and Probabilistic Mathematics) (Paperback)
Great book for an applied or a theoretical statistician. Particularly helpful for graduate students as a tool for research.
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First Sentence:
Why asymptotic statistics? Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
efficient influence function, portmanteau lemma, asymptotic representation theorem, efficient score function, normal limit experiment, rescaling rate, most powerful scores, efficient score equation, local power functions, bracketing numbers, estimator sequence, tangent set, preceding display, asymptotic optimality theory, marginal convergence, smooth parametric model, asymptotic power functions, functional delta method, likelihood ratio process, limiting power function, asymptotic quality, local asymptotic normality, simple linear rank statistics, log poo, score operator Key Phrases - Capitalized Phrases (CAPs): (learn more)
Bernstein-von Mises, Introduction Suppose New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Why asymptotic statistics? Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
efficient influence function, portmanteau lemma, asymptotic representation theorem, efficient score function, normal limit experiment, rescaling rate, most powerful scores, efficient score equation, local power functions, bracketing numbers, estimator sequence, tangent set, preceding display, asymptotic optimality theory, marginal convergence, smooth parametric model, asymptotic power functions, functional delta method, likelihood ratio process, limiting power function, asymptotic quality, local asymptotic normality, simple linear rank statistics, log poo, score operator Key Phrases - Capitalized Phrases (CAPs): (learn more)
Bernstein-von Mises, Introduction Suppose 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 31
books:
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71
books
cite this book:
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- Robust Statistics (Wiley Series in Probability and Statistics) by Peter J. Huber in Back Matter (1), and Back Matter (2)
- Mathematical Statistics: Basic Ideas and Selected Topics, Vol I (2nd Edition) by Peter J. Bickel in Back Matter
- Probability Theory (De Gruyter Studies in Mathematics) by Heinz Bauer in Back Matter
- Higher Order Asymptotics (NSF-CBMS regional conference series in probability and statistics) by J. K. Ghosh in Back Matter
- A Guide to Chi-Squared Testing (Wiley Series in Probability and Statistics) by Priscilla E. Greenwood in Back Matter
See all 31 books this book cites
- Econometric Foundations Pack with CD-ROM by Ron C. Mittelhammer on page 130, page 156, and page 195
- Asymptotics in Statistics: Some Basic Concepts (Springer Series in Statistics) by Lucien Le Cam on page 5, Back Matter (1), and Back Matter (2)
- Breakthroughs in Statistics: Volume III (Springer Series in Statistics / Perspectives in Statistics) by Samuel Kotz on page 329, and Back Matter
- The Coordinate-Free Approach to Linear Models (Cambridge Series in Statistical and Probabilistic Mathematics) by Michael J. Wichura in Front Matter, and Back Matter
- Theory of Valuation by Sudipto Bhattacharya on page 23, and page 43
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