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