IMPROVING BAYESIAN ESTIMATION OF THE END POINT OF A DISTRIBUTION

Yuta Minoda, T. Kamakura, T. Yanagimoto
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Abstract

Bayesian estimation of the end point of a distribution is proposed and examined. For this problem, it is well known that the maximum likelihood method does not work well. By modifying the prior density in Hall and Wang (2005) and applying marginal inference, we derive estimators superior to existing ones. The proposed estimators are closely related to the estimating functions which are known to outperform maximum likelihood equations. Another advantage of the proposed method is to resolve the convergence problem. Our simulation results strongly support the superiority of the proposed estimators over the existing ones under the mean squared error. Illustrative examples are also given.
改进分布终点的贝叶斯估计
提出并检验了分布终点的贝叶斯估计。对于这个问题,众所周知,极大似然法并不适用。通过修改Hall和Wang(2005)中的先验密度并应用边际推理,我们得到了优于现有估计器的估计器。所提出的估计量与已知优于极大似然方程的估计函数密切相关。该方法的另一个优点是解决了收敛性问题。我们的仿真结果有力地支持了在均方误差下所提出的估计器比现有估计器的优越性。并给出了实例说明。
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