A Note on Comparison of Restricted and Unrestricted Estimators in Estimating Linear Functions of Ordered Scale Parameters of Two Gamma Distributions

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 comparison between MLE and modified MLE is also mentioned. A sufficient condition of two coefficients is also given for modified MLE to dominate the MLE, when two shape parameters are the same. 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.