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Asymptotic normality of test statistics under alternative hypotheses

Alexander Shapiro ()

Journal of Multivariate Analysis, 2009, vol. 100, issue 5, 936-945

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.

Keywords: primary; 62F05 secondary; 62H25; 62E20 Stochastic optimization Likelihood ratio test statistic Asymptotic normality Asymptotic bias Nonnested models Moment (covariance) structures Discrepancy functions (search for similar items in EconPapers)
Date: 2009
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