基于无信息先验的分层指数模型参数在Stein损失 函数下的贝叶斯估计

Bayesian Estimation of Exponential Distribution Parameters Based on Uninformed Priori under Stein Loss Function

参数估计问题是数理统计学中研究较多的一类问题。本文是基于一个无信息先验的分层指数模型在Stein损失函数下的贝叶斯估计。首先计算分层指数模型分别在平方误差损失函数和Stein损失函数下的贝叶斯后验估计量和相应的后验期望Stein损失(PESL),并且比较二者在两个损失函数下的大小。可以看出在Stein损失函数下的贝叶斯后验期望和对应的PESL均略小于平方误差损失函数下的相应量。然后,计算分层指数模型的参数在Stein损失函数下的贝叶斯估计,并通过均方误差来评价估计量的好坏,得出后验期望估计量拟合得最好。最后通过随机数值和我国31个省市自治区的结婚数据对以上理论进行了模拟和实证,说明了该模型和方法的有效性和实用性。

Parameter estimation is one of the most studied problems in mathematical statistics.This paper is based on the Bayesian estimation of a hierarchical exponential model under the Stein loss function.Firstly,the Bayesian posterior estimations and the corresponding posterior expected loss(PESL)of the hierarchical exponential model are calculated under the Square error loss function and the Stein loss function respectively,and the magnitude of them under the two loss function are compared.It can be seen that the Bayesian posterior estimations and the posterior expected loss(PESL)under the Stein loss function are slightly smaller than the corresponding quantity under the Square error loss function.Then,the Bayesian estimations of the parameter of the hierarchical exponential model under the Stein loss function are calculated,and the quality of estimator are evaluated by means of the mean Square error,and the posterior expected estimator is the best fit.Firstly,the above theory are simulated and verified by random values and the marriage rate data of 31 provinces and autonomous regions in China,which shows that both this model and method are useful and effective.