Finite-sample inference with monotone incomplete multivariate normal data, II |
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Authors: | Wan-Ying Chang |
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Institution: | a Washington Department of Fish and Wildlife, Olympia, WA 98501, USA b Department of Statistics, Penn State University, University Park, PA 16802, USA c The Statistical and Applied Mathematical Sciences Institute, Research Triangle Park, NC 27709, USA |
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Abstract: | We continue our recent work on inference with two-step, monotone incomplete data from a multivariate normal population with mean and covariance matrix . Under the assumption that is block-diagonal when partitioned according to the two-step pattern, we derive the distributions of the diagonal blocks of and of the estimated regression matrix, . We represent in terms of independent matrices; derive its exact distribution, thereby generalizing the Wishart distribution to the setting of monotone incomplete data; and obtain saddlepoint approximations for the distributions of and its partial Iwasawa coordinates. We prove the unbiasedness of a modified likelihood ratio criterion for testing , where is a given matrix, and obtain the null and non-null distributions of the test statistic. In testing , where and are given, we prove that the likelihood ratio criterion is unbiased and obtain its null and non-null distributions. For the sphericity test, , we obtain the null distribution of the likelihood ratio criterion. In testing we show that a modified locally most powerful invariant statistic has the same distribution as a Bartlett-Pillai-Nanda trace statistic in multivariate analysis of variance. |
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Keywords: | Primary 62H10 secondary 60D10 62E15 |
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