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

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Format
Hardback, 357 pages
Published
United States, 4 May 2010

Providing a broad toolkit of analytical methods, this book 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. It describes core ideas in statistical asymptotics; covers Laplace approximation, the saddle-point method, and summation of series; and includes vignettes of various people from statistics and mathematics whose ideas have been instrumental in the development of the subject. The author also supplements some topics with relevant Maplea commands and provides a list of common series and products, enabling readers to expand an expression or simplify an expansion.


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Product Description

Providing a broad toolkit of analytical methods, this book 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. It describes core ideas in statistical asymptotics; covers Laplace approximation, the saddle-point method, and summation of series; and includes vignettes of various people from statistics and mathematics whose ideas have been instrumental in the development of the subject. The author also supplements some topics with relevant Maplea commands and provides a list of common series and products, enabling readers to expand an expression or simplify an expansion.

Product Details
EAN
9781584885900
ISBN
1584885904
Other Information
28 black & white illustrations, 3 black & white tables
Dimensions
23.9 x 15.8 x 2.3 centimeters (0.66 kg)

Table of Contents

Introduction. General Series Methods. Padé 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.

About the Author

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

Reviews

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, Praha, in 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, E-MADAS; Madrid, in Mathematical Reviews

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