The effects of nonnormality on asymptotic distributions of some likelihood ratio criteria for testing covariance structures under normal assumption

This paper examines asymptotic distributions of the likelihood ratio criteria, which are proposed under normality, for several hypotheses on covariance matrices when the true distribution of a population is a certain nonnormal distribution. It is well known that asymptotic distributions of test statistics depend on the fourth moments of the true population's distribution. We study the effects of nonnormality on the asymptotic distributions of the null and nonnull distributions of likelihood ratio criteria for covariance structures.Asymptotic distribution Fixed alternative Kurtosis Local alternative Model misspecification with respect to distribution Nonnormality Nonnull distribution Null distribution Robustness Testing for covariance structures vecs operator Weighted sum of chi-squared variables