Expansions and Asymptotics for Statistics [Hardcover]

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 Statisticsshows 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.

Introduction
Expansions and approximations
The role of asymptotics
Mathematical preliminaries
Two complementary approaches

General Series Methods
A quick overview
Power series
Enveloping series
Asymptotic series
Superasymptotic and hyperasymptotic series
Asymptotic series for large samples
Generalised asymptotic expansions
Notes

Pad? Approximants and Continued Fractions
The Pad? table
Pad? approximations for the exponential function
Two applications
Continuedlc-