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Asymptotic nonnull distributions of certain test criteria for a covariance matrix |
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| Authors: | Hisao Nagao |
| Institution: | Department of Mathematics, Faculty of General Education, Kumamoto University, Kumamoto, Japan |
| Abstract: | Asymptotic expansions of the distributions of two test criteria concerning a covariance matrix are derived under local alternatives in terms of noncentral χ2 variates, and under the fixed alternative in terms of standard normal distribution function and its derivatives, respectively. Some numerical comparisons with the likelihood ratio criteria are made with these test criteria. |
| Keywords: | Sphericity test local alternatives fixed alternative locally best invariant test characteristic function asymptotic expansions likelihood ratio test power function |
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