AISM 54, 848-860

© 2002 ISM

## A comparison of restricted and unrestricted estimators in estimating linear functions of ordered scale parameters of two gamma distributions

### Yuan-Tsung Chang^{1} and Nobuo Shinozaki^{2}

^{1}Department of Studies on Contemporary Society,
Mejiro University, Iwatsuki, Saitama 339-8501, Japan

^{2}Department of Administration Engineering, Faculty of
Science and Technology, Keio University, Yokohama, Kanagawa 223-8522, Japan

(Received May 15, 2000; revised September 25, 2001)

Abstract.
The problem of estimating linear functions of ordered
scale parameters of two Gamma distributions is considered. A
necessary and sufficient condition on the ratio of two
coefficients is given for the maximum likelihood estimator (MLE)
to dominate the crude unbiased estimator (UE) in terms of mean
square error. A modified MLE which satisfies the restriction is
also suggested, and a necessary and sufficient condition is
also given for it to dominate the admissible estimator based
solely on one sample. The estimation of linear functions of
variances in two sample problem and also of variance components
in a one-way random effect model is mentioned.

Key words and phrases:
MLE, unbiased estimator, admissible estimator, variance estimation.

**Source**
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