Expansions and Asymptotics for Statistics - Couverture rigide

Small, Christopher G.

Couverture rigide

ISBN 10 : 1584885904 ISBN 13 : 9781584885900

Editeur : Routledge, 2010

Synopsis

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. Cramér, 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.

A propos du livre

À propos de l'auteur

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

À propos de la quatrième de couverture

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 Maple(TM) commands and provides a list of common series and products, enabling readers to expand an expression or simplify an expansion.

Détails de l'édition

• Éditeur: Routledge
• Date d'édition: 2010
• Langue: anglais
• ISBN 10: 1584885904
• ISBN 13: 9781584885900
• Reliure: Relié
• Nombre de pages: 343
• Coordonnées du fabricant: non disponible
• Personne responsable: gpsr@libri.de; gpsr@libri.de; ; Europaallee 1; Bad Hersfeld; 36244; Allemagne