Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1147108 | Journal of Multivariate Analysis | 2009 | 10 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Numerical Analysis
Authors
Alexander Shapiro,