两种统计框架下均匀分布参数估计的对比研究  

Comparative Studies of Parameter of Uniform Distribution in the Two Framework of Statistic

作　　者：徐宝[1] 王瑞鸿 祁鹤 王迪 Xu Bao;Wang Ruihong;Qi He;Wang Di(Institute of Mathematics,Jilin Normal University,Siping 136000,China)

机构地区：[1]吉林师范大学数学学院,吉林四平136000

出　　处：《南开大学学报（自然科学版）》2021年第5期30-35,共6页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：国家自然科学基金(11571138)。

摘　　要：在理论和模拟方面对均匀分布U(0,θ)参数θ的Bayes估计与极大似然估计进行对比研究.首先将基于损失函数和共轭先验得到的Bayes估计与极大似然估计在形式上进行对比,发现所得Bayes估计不但在数值上略大于极大似然估计,而且还是参数的相应函数的极大似然估计;然后通过模拟研究两种估计方法对参数的返真性,结果表明所得的Bayes估计的均方误差在大多数场合下都小于极大似然估计的均方误差.The comparisons between the Bayesian estimation and the maximum likelihood estimation are studied from theory and simulation respectively.First,the comparison is carrying out form the form of the maximum likelihood estimation and the Bayesian estiomation which obtained on the basis of the Pareto conjugate prior distribution and the loss function,the Bayesian estimation is not only larger than the maximum likelihood estimation but also the maximum likelihood estimations of the corresponding functions of the parameter.Then a simulation investigation is conducted to evaluate the performance of the Bayesian estimation and the maximum likelihood estimation,it’s shown that the MSE of the Bayesian estimation is smaller than the MSE of the maximum likelihood estimation on most of occasion.

关 键 词：均匀分布 BAYES估计 损失函数 共轭先验分布 极大似然估计 

分 类 号：O212[理学—概率论与数理统计]