LINEX损失下双指数分布位置参数的经验Bayes估计

The Empirical Bayes Estimation of the Location Parameter in Double-Exponential Family under the LINEX Loss Function

摘要: 本文对双指数分布在LINEX损失函数下获得了位置参数的Bayes估计, 同时构造了相应的经验Bayes估计, 证明了所提出的经验Bayes估计是渐近最优的, 且有收敛速度, , 其中1/2<r<1-1/(2s), 而是任意给定的整数. 最后给出一个例子说明适合定理条件的先验分布是存在的.

Abstract: In this paper, we derive the Bayes estimator of the location parameter in double-exponential family under the LINEX loss function, and then construct the corresponding empirical Bayes estimator. It is shown that the empirical Bayes estimator is asymptotically optimal with convergence rate being , , where 1/2<r<1-1/(2s), while is a given integer. Finally, an example is demonstrated.