线性指数模型参数的经验贝叶斯估计

根据经验贝叶斯原理,讨论了在平方损失函数下,线性指数模型参数的非参数经验贝叶斯(empirical贝叶斯,EB)估计问题.首先利用密度函数的核估计方法构造边际分布密度函数以及该分布密度函数的一阶导数;然后结合线性指数模型未知参数在相同损失函数之下的贝叶斯估计得到了未知参数的非参数经验贝叶斯估计.最后由C-R不等式以及Jensen不等式证明了所得到的经验贝叶斯估计的渐进最优性质,并获得了其收敛速度(n-(2r-1)/(2r 1)).

Estimation of the parameters of linear exponential model by empirical Bayes

By means of empirical Bayesian principle,a nonparametric empirical Bayes estimator of the unknown parameter was discussed under the square loss function for the linear exponential model.The marginal distribute density function and its first order derivative were constructed by using kernel estimation method.In combination with the Bayes estimator for the parameter of linear exponential model under the same loss function,the nonparametric empirical Bayes estimator of the unknown parameter was obtained.It was proved that the proposed estimator was an asymptotical EB estimator according to C-R inequality and Jensen inequality,and the convergence rate was established.