CIRJE-F-264 | "A Revisit to Estimation of the Precision Matrix of the Wishart Distribution" |
Author Name | Kubokawa, Tatsuya |
Date | February 2004 |
Full Paper | PDF file@ |
Remarks | @Revised in March 2004; subsequently published in Journal of Statistical Research (2005), 39, 97-120. |
Abstract |
The estimation of the precision matrix of the Wishart distribution is one of classical problems studied in a decision-theoretic framework and is related to estimation of mean and covariance matrices of a multivariate normal distribution. This paper revisits the estimation problem of the precision matrix and investigates how it connects with the theory of the covariance estimation from a decision-theoretic aspect. To evaluate estimators in terms of risk functions, we employ two kinds of loss functions: the non-scale-invariant loss and the scale-invariant loss functions which are induced from estimation of means. Using the same methods as in the estimation of the covariance matrix, we derive not only the James-Stein type of estimators improving on the Stein type one under the non-scale-invariant loss. It is observed that dominance properties given in the estimation of the covariance matrix do not necessarily hold in our setup under the non-scale-invariant loss, but still hold relative to the scale-invariant loss. The simulation studies are given, and estimators having superior risk performances are proposed. |