*J. Japan Statist. Soc.,* Vol. 35 (No. 1), pp. 21-39, 2005

## Estimating the Inverse Matrix of Scale Parametersin an Elliptically Contoured Distribution

Hisayuki Tsukuma

**Abstract. **
The problem of estimating the inverse matrix of scale parameters of an elliptically contoured distribution is considered with respect to Stein's loss function. It is shown that improvemen of the estimators obtained under the normality assumption remains robust under an elliptically contoured distribution. A numerical study is also conducted to evaluate the risk performances of the improved estimators.

*Key words and phrases*:
Elliptically contoured distribution, expected value, multivariate linear model, precision matrix, Stein's loss.

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