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Estimation of two ordered normal means when a covariance matrix is known |
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| Authors: | Yuan-Tsung Chang Kazufumi Fukuda Nobuo Shinozaki |
| Institution: | 1. Department of Social Information, Mejiro University, Tokyo, Japan;2. Department of Pure and Applied Mathematics, Graduate School of Fundamental Science and Engineering, Waseda University, Tokyo, Japan;3. Faculty of Science and Technology, Keio University, Yokohama, Japan |
| Abstract: | Estimation of two normal means with an order restriction is considered when a covariance matrix is known. It is shown that restricted maximum likelihood estimator (MLE) stochastically dominates both estimators proposed by Hwang and Peddada Confidence interval estimation subject to order restrictions. Ann Statist. 1994;22(1):67–93] and Peddada et al. Estimation of order-restricted means from correlated data. Biometrika. 2005;92:703–715]. The estimators are also compared under the Pitman nearness criterion and it is shown that the MLE is closer to ordered means than the other two estimators. Estimation of linear functions of ordered means is also considered and a necessary and sufficient condition on the coefficients is given for the MLE to dominate the other estimators in terms of mean squared error. |
| Keywords: | Ordered normal means MLE stochastical domination Pitman nearness criterion mean squared error |