Estimation of Ordered Means of Two Poisson Distributions |
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Authors: | Yuan-Tsung Chang Nobuo Shinozaki |
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Institution: | 1. Department of Studies on Contemporary Society , Mejiro University , Saitama , Japan cho@mejiro.ac.jp;3. Department of Administration Engineering , Keio University , Yokohama , Japan |
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Abstract: | In this article, we discuss the estimation of linear functions of two Poisson means, on which an order restriction is given. We give a necessary and sufficient condition on the coefficients of the linear function for the maximum likelihood estimator (MLE) which satisfies the order restriction to dominate the unbiased estimator under squared error loss. Furthermore, simultaneous estimation of two ordered Poisson means is considered and we suggest the Clevenson–Zidek type modification of MLE which dominates the MLE under normalized squared error loss. We also improve the estimator proposed by Clevenson and Zidek (1975
Clevenson , M. ,
Zidek , J. ( 1975 ). Simultaneous estimation of the means of independent Poisson laws . J. Amer. Statist. Assoc. 70 : 698 – 705 . CSA] CROSSREF] Taylor & Francis Online], Web of Science ®] , Google Scholar]) which ignores the order restriction. |
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Keywords: | MLE Squared error loss Unbiased estimator Uniform improvement |
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