Asymptotic Expansions of the Non-Null Distributions of Likelihood Ratio Criteria for Covariance Matrices
Asymptotic Expansions of the Non-Null Distributions of Likelihood Ratio Criteria for Covariance Matrices
In this paper, asymptotic expansions of the non-null distributions of the likelihood ratio criteria are obtained for testing the hypotheses: (a) $H_1: \Sigma = \sigma^2I, \sigma^2 > 0$, (b) $H_2: \Sigma_1 = \Sigma_2$, against alternatives which are close to the hypothesis. These expansions are of chi-square type. The first problem …