Error bounds for high–dimensional Edgeworth expansions for some tests on covariance matrices
نویسنده
چکیده
Problems of testing three hypotheses : (i) equality of covariance matrices of several multivariate normal populations, (ii) sphericity, and (iii) that a covariance matrix is equal to a specified one, are treated. High–dimensional Edgeworth expansions of the null distributions of the modified likelihood ratio test statistics are derived. Computable error bounds of the expansions are derived for each expansions. The Edgeworth expansion and its error bound for non–null distribution of the test statistic for (iii) are also derived.
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