Expansions and Asymptotics for Statistics
1st Edition
Published on 7. May 2010
Book
Hardback
357 pages
978-1-58488-590-0 (ISBN)
Description
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.
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.
Reviews / Votes
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 Gutierrez-Pena, 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 MATHThis 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 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 Gutierrez-Pena, International Statistical Review, 2012
his 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 MATHThis 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
More details
Series
Language
English
Place of publication
Oxford
United States
Publishing group
Taylor & Francis Inc
Target group
Professional and scholarly
Professional
Product notice
Paper over boards
Illustrations
28 s/w Abbildungen, 3 s/w Tabellen
3 Tables, black and white; 28 Illustrations, black and white
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 24 mm
Weight
702 gr
ISBN-13
978-1-58488-590-0 (9781584885900)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Christopher G. Small
Expansions and Asymptotics for Statistics
E-Book
05/2010
Chapman and Hall
€225.99
Available for download
Christopher G. Small
Expansions and Asymptotics for Statistics
E-Book
05/2010
1st Edition
Chapman & Hall/CRC
€225.99
Available for download
Person
Christopher G. Small is a professor in the Department of Statistics and Actuarial Science at the University of Waterloo in Ontario, Canada.
Content
Introduction. General Series Methods. Pade Approximants and Continued Fractions. The Delta Method and Its Extensions. Optimality and Likelihood Asymptotics. The Laplace Approximation and Series. The Saddle-Point Method. Summation of Series. Glossary of Symbols. Useful Limits, Series and Products. References. Index.