Asymptotics in General

Abstract

Many authors have examined the use of asymptotic methods in statistics. Serfling (1980) investigates applications of probability limit theorems for distributions of random variables, including theorems concerning convergence almost surely, to many questions in applied statistics. Le Cam (1969) treats asymptotics from a decision-theoretic viewpoint. Barndorff-Nielsen and Cox (1989) present many applications of the density and distribution function approximations to be described below in a heuristic manner. Hall (1992) investigates Edgeworth series with a particular view towards applications to the bootstrap. Field and Ronchetti (1990) treat series expansion techniques in a manner that most closely parallels this work; I have included more detailed proofs and discussion of regularity conditions, and a survey of the use of Barndorff-Nielsen’s formula. Their work covers many aspects of robustness and estimating equations not included here. Skovgaard (1990) explores characteristics of models making them amenable to asymptotic techniques, and derives the concept of an analytic statistical model. He also investigates convergence along series indexed by more general measures of information than sample size.