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Expansions and Asymptotics for Statistics : Chapman & Hall/CRC Monographs on Statistics and Applied Probability - Christopher G. Small

Expansions and Asymptotics for Statistics

By: Christopher G. Small

Hardcover | 7 May 2010 | Edition Number 1

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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. Cram r, 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.

Industry 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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