Expansions and Asymptotics for Statistics

This book provides a broad toolkit of analytical methods and implements the topics with relevant Maple'„¢ commands. It first presents methods for expansions of functions arising in probability and statistics. The text then describes mainstream statistical asymptotics, namely the asymptotic normality and asymptotic efficiency of standard estimators as the sample size goes to infinity. After focusing on Laplace approximation and the saddle-point method, the author discusses alternatives to Monte Carlo techniques, such as the summation of series. Throughout the text, he also includes vignettes of various instrumental people in statistics and mathematics.