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Bayes Empirical Bayes Estimation for Scale Parameter

Lichun Wang

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Abstract

We employ the Bayes empirical Bayes (EB) procedure to estimate the scale parameter in a special exponential family,and prove that the Bayes EB estimator of the scale parameter converges almost surely (a.s.) to its Bayes estimator and it is asymptotically optimal. Also,a simulation experiment is conducted to demonstrate the asymptotic optimality of the Bayes EB estimator.

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What this paper is about

We employ the Bayes empirical Bayes (EB) procedure to estimate the scale parameter in a special exponential family,and prove that the Bayes EB estimator of the scale parameter converges almost surely (a.s.) to its Bayes estimator and it is asymptotically optimal. Also,a simulation experiment is conducted to demonstrate the asymptotic optimality of the Bayes EB estimator.

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Available abstract

We employ the Bayes empirical Bayes (EB) procedure to estimate the scale parameter in a special exponential family,and prove that the Bayes EB estimator of the scale parameter converges almost surely (a.s.) to its Bayes estimator and it is asymptotically optimal. Also,a simulation experiment is conducted to demonstrate the asymptotic optimality of the Bayes EB estimator.

Key concepts: Bayes' theorem, Mathematics, Estimator, Bayes estimator, Scale parameter, Bayes' rule, Bayes error rate, Scale (ratio)

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