Estimation of means of multivariate normal populations with order restriction |
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Authors: | Tiefeng Ma Songgui Wang |
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Affiliation: | a Statistics College, Southwestern University of Finance and Economics, Chengdu, 610074, China b Department of Applied Mathematics, Beijing University of Technology, Beijing, 100124, China |
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Abstract: | Multivariate isotonic regression theory plays a key role in the field of statistical inference under order restriction for vector valued parameters. Two cases of estimating multivariate normal means under order restricted set are considered. One case is that covariance matrices are known, the other one is that covariance matrices are unknown but are restricted by partial order. This paper shows that when covariance matrices are known, the estimator given by this paper always dominates unrestricted maximum likelihood estimator uniformly, and when covariance matrices are unknown, the plug-in estimator dominates unrestricted maximum likelihood estimator under the order restricted set of covariance matrices. The isotonic regression estimators in this paper are the generalizations of plug-in estimators in unitary case. |
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Keywords: | primary, 62F30 secondary, 62H12 |
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