# Expansions and Asymptotics for Statistics (Chapman & Hall/CRC Monographs on Statistics & Applied Probability)

## Christopher G. Small

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Asymptotic methods provide important tools for approximating and analysing functions that arise in probability and statistics. Moreover, the conclusions of asymptotic analysis often supplement the conclusions obtained by numerical methods. Providing a broad toolkit of analytical methods, Expansions and Asymptotics for Statistics shows how asymptotics, when coupled with numerical methods, becomes a powerful way to acquire a deeper understanding of the techniques used in probability and statistics.

The book first discusses the role of expansions and asymptotics in statistics, the basic properties of power series and asymptotic series, and the study of rational approximations to functions. With a focus on asymptotic normality and asymptotic efficiency of standard estimators, it covers various applications, such as the use of the delta method for bias reduction, variance stabilisation, and the construction of normalising transformations, as well as the standard theory derived from the work of R.A. Fisher, H. Cramér, L. Le Cam, and others. The book then examines the close connection between saddle-point approximation and the Laplace method. The final chapter explores series convergence and the acceleration of that convergence.

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Christopher G. Small is a professor in the Department of Statistics and Actuarial Science at the University of Waterloo in Ontario, Canada.

Review:

This book will be an excellent resource for researchers and graduate students who need a deeper understanding of functions arising in probability and statistics than that provided by numerical techniques.
―Eduardo Gutiérrez-Peña, International Statistical Review, 2012

This outstanding book is rich in contents and excellent in readability. ... I enjoyed reading this book and found this book valuable in my research as well as in my understanding of expansions and asymptotics as they arise often in statistics. The author has to be commended for his contribution to our profession in getting this book out.
―Subir Ghosh, Technometrics, May 2012

I have found this book very useful not only for the specialists in asymptotics but especially for all those who wish to learn more from this field and to see the inter-relations between different approaches.
―Jaromir Antoch, Zentralblatt MATH

This is an excellent book for researchers interested in asymptotics, especially those working on (mathematical) statistics or applied probability. ... The book contains a compilation of different techniques to deal with series expansions and approximations with statistical applications. Examples are focused on the approximation of probability densities, distributions and likelihoods.
―Javier Carcamo, Mathematical Reviews

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## 1.Expansions and Asymptotics for Statistics

ISBN 10: 1584885904 ISBN 13: 9781584885900
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Descripción 2010. HRD. Estado de conservación: New. New Book. Shipped from US within 10 to 14 business days. Established seller since 2000. Nº de ref. de la librería VT-9781584885900

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## 2.Expansions and Asymptotics for Statistics (Chapman & Hall/CRC Monographs on Statistics & Applied Pro

Editorial: Chapman and Hall/CRC (2010)
ISBN 10: 1584885904 ISBN 13: 9781584885900
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Descripción Chapman and Hall/CRC, 2010. Hardcover. Estado de conservación: New. Never used!. Nº de ref. de la librería P111584885904

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## 3.Expansions and Asymptotics for Statistics

Editorial: Chapman and Hall/CRC (2010)
ISBN 10: 1584885904 ISBN 13: 9781584885900
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Descripción Chapman and Hall/CRC, 2010. Hardback. Estado de conservación: NEW. 9781584885900 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. For all enquiries, please contact Herb Tandree Philosophy Books directly - customer service is our primary goal. Nº de ref. de la librería HTANDREE0185990

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## 4.Expansions and Asymptotics for Statistics (Hardback)

Editorial: Taylor Francis Inc, United States (2010)
ISBN 10: 1584885904 ISBN 13: 9781584885900
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Descripción Taylor Francis Inc, United States, 2010. Hardback. Estado de conservación: New. New.. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. Asymptotic methods provide important tools for approximating and analysing functions that arise in probability and statistics. Moreover, the conclusions of asymptotic analysis often supplement the conclusions obtained by numerical methods. Providing a broad toolkit of analytical methods, Expansions and Asymptotics for Statistics shows how asymptotics, when coupled with numerical methods, becomes a powerful way to acquire a deeper understanding of the techniques used in probability and statistics. The book first discusses the role of expansions and asymptotics in statistics, the basic properties of power series and asymptotic series, and the study of rational approximations to functions. With a focus on asymptotic normality and asymptotic efficiency of standard estimators, it covers various applications, such as the use of the delta method for bias reduction, variance stabilisation, and the construction of normalising transformations, as well as the standard theory derived from the work of R.A. Fisher, H. Cramer, L. Le Cam, and others. The book then examines the close connection between saddle-point approximation and the Laplace method. The final chapter explores series convergence and the acceleration of that convergence. Nº de ref. de la librería BTE9781584885900

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## 5.Expansions and Asymptotics for Statistics

Editorial: Chapman & Hall (2010)
ISBN 10: 1584885904 ISBN 13: 9781584885900
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Descripción Chapman & Hall, 2010. Hardcover. Estado de conservación: Brand New. 1st edition. 357 pages. 9.69x6.50x0.91 inches. In Stock. Nº de ref. de la librería __1584885904

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## 6.Expansions and Asymptotics for Statistics (Chapman & Hall/CRC Monographs on Statistics & Applied Probability)

Editorial: Chapman and Hall/CRC (2010)
ISBN 10: 1584885904 ISBN 13: 9781584885900
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Descripción Chapman and Hall/CRC, 2010. Estado de conservación: New. Nº de ref. de la librería TV9781584885900

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## 7.Expansions and Asymptotics for Statistics (Hardcover)

ISBN 10: 1584885904 ISBN 13: 9781584885900
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Descripción 2010. Hardcover. Estado de conservación: New. Hardcover. includes vignettes of various instrumental people in statistics and Providing a toolkit of analytical methods, this book shows how asymptotics, when coupled with numerical met.Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. 357 pages. 0.656. Nº de ref. de la librería 9781584885900

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