"Estimation and Prediction Intervals in Transformed Linear Mixed Models"
   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.
Year of publication: |
2014-04
|
---|---|
Authors: | Tsukuma, Hisayuki ; Kubokawa, Tatsuya |
Institutions: | Center for International Research on the Japanese Economy (CIRJE), Faculty of Economics |
Saved in:
freely available
Saved in favorites
Similar items by person
-
"Minimaxity in Estimation of Restricted and Non-restricted Scale Parameter Matrices"
Tsukuma, Hisayuki, (2012)
-
"Unified Improvements in Estimation of a Normal Covariance Matrix in High and Low Dimesions"
Tsukuma, Hisayuki, (2014)
-
"A Unified Approach to Estimating a Normal Mean Matrix in High and Low Dimensions"
Tsukuma, Hisayuki, (2014)
- More ...