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Improving on truncated linear estimates of exponential and gamma scale parameters. (English) Zbl 0846.62006
Summary: We consider the problem of estimating the scale parameter of an exponential or a gamma distribution under squared error loss when the scale parameter \(\theta\) is known to be greater than some fixed value \(\theta_0\). Natural estimators in this setting include truncated linear functions of the sufficient statistic. Such estimators are typically inadmissible, but explicit improvements seem difficult to find. Some are presented here. A particularly interesting finding is that estimators which are admissible in the untruncated problem which take values only in the interior of the truncated parameter space are found to be inadmissible for the truncated problem.

MSC:
62C15 Admissibility in statistical decision theory
62F10 Point estimation
62C99 Statistical decision theory
62F30 Parametric inference under constraints
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