Expansions and Asymptotics for Statistics

ISBN-13: 9781584885900 / Angielski / Twarda / 2010 / 357 str.

Christopher G Small

Opis

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."

Spis treści

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.

O autorze

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