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This paper shows some simple shrunken estimators for the scale parameter of an exponential distribution and compares them with minimum MSE estimator and the estimator proposed by Pandey We have also obtained a Bayes estimator, which is a shrinkage estimator and has smaller MSE than the estimator (sample mean) n/(n + 1) if sample size, n, is small and other restrictions apply.
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Pandey et al. (1985) studied this question.
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