Asymptotic normality of test statistics under alternative hypotheses

Authors:
Alexander Shapiro
Affiliations:
School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0205, USA
Venue:
Journal of Multivariate Analysis
Year:
2009

Citing 2
Cited 0

Asymptotic analysis of stochastic programs

Annals of Operations Research
Normal theory likelihood ratio statistic for mean and covariance structure analysis under alternative hypotheses

Journal of Multivariate Analysis

Quantified Score

Hi-index	0.00

Visualization

Abstract

The aim of this paper is to present a framework for asymptotic analysis of likelihood ratio and minimum discrepancy test statistics. First order asymptotics are presented in a general framework under minimal regularity conditions and for not necessarily nested models. In particular, these asymptotics give sufficient and in a sense necessary conditions for asymptotic normality of test statistics under alternative hypotheses. Second order asymptotics, and their implications for bias corrections, are also discussed in a somewhat informal manner. As an example, asymptotics of test statistics in the analysis of covariance structures are discussed in detail.