Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Hierarchical and Empirical Bayes Estimators of Gamma Parameter under Entropy Loss

  • Published : 1999.04.01
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Abstract

Let be $X_1$,...,$X_p$, $p\geq2$ independent random variables where each $X_i$ has a gamma distribution with $\textit{k}_i$ and $\theta_i$ The problem is to simultaneously estimate $\textit{p}$ gamma parameters $\theta_i$ and $\theta_i{^-1}$ under entropy loss where the parameters are believed priori. Hierarch ical Bayes(HB) and empirical Bayes(EB) estimators are investigated. And a preference of HB estimator over EB estimator is shown using Gibbs sampler(Gelfand and Smith 1990). Finally computer simulation is studied to compute the risk percentage improvements of the HB estimator and the estimator of Dey Ghosh and Srinivasan(1987) compared to UMVUE estimator of $\theta^{-1}$.

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References

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