针对偏正态混合效应模型, 研究模型固定效应和偏度参数的经验贝叶斯估计问题. 首先, 基于固定效应和偏度参数的先验分布及贝叶斯法则, 给出其后验分布. 进而, 综合运用极大似然估计方法和MCMC技术, 获得固定效应和偏度参数的经验贝叶斯估计及其算法. 模拟结果表明, 在均方误差意义下, 经验贝叶斯估计在大部分情况下优于由Nelder-Mead算法获得的极大似然估计. 最后, 将经验贝叶斯估计应用于中国长三角城市群人口增长的影响因素分析.

In this study, the empirical Bayesian estimation of fixed effect and skewness parameter are discussed for the skew-normal mixed effects model. Based on the prior distribution of the parameters and Bayes law, the posterior distributions of the parameters are given. Furthermore, the empirical Bayesian estimates and algorithms of fixed effect and skewness parameter are obtained by using maximum likelihood estimation and MCMC technology. The simulation results show that the empirical Bayesian estimates are better than the maximum likelihood estimates obtained by the Nelder-Mead method in most cases in the sense of mean squared error. Finally, the empirical Bayesian estimation is applied to the analysis of the influencing factors of population growth in the Yangtze River Delta urban agglomeration in China.