Estimation and Prediction Intervals in Transformed Linear Mixed Models

Hisayuki Tsukuma and Tatsuya Kubokawa
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Hisayuki Tsukuma: Faculty of Medicine, Toho University
Tatsuya Kubokawa: Faculty of Economics, The University of Tokyo

No CIRJE-F-930, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: 　　 This paper addresses the problem of estimating the mean vector of a singular multivariate normal distribution with an unknown singular covariance matrix. The maximum likelihood estimator is shown to be minimax relative to a quadratic loss weighted by the Moore-Penrose inverse of the covariance matrix. An unbiased risk estimator relative to the weighted quadratic loss is provided for a Baranchik type class of shrinkage estimators. Based on the unbiased risk estimator, a sufficient condition for the minimaxity is expressed not only as a differential inequality, but also as an integral inequality. Also, generalized Bayes minimax estimators are established by using an interesting structure of singular multivariate normal distribution.

Pages: 23 pages
Date: 2014-04
New Economics Papers: this item is included in nep-ecm
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Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2014cf930

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