带有偏正态误差的众数回归模型最大似然估计的EM算法  

Parameter estimates for mean and mode regression models with skew-normal errors

作　　者：姜喆 王丹璐 吴刘仓[1,2] JIANG Zhe;WANG Dan-lu;WU Liu-cang(Faculty of Science,Kunming University of Science and Technology,Kunming 650500,China;Center for Applied Statistics,Kunming University of Science and Technology,Kunming 650500,China)

机构地区：[1]昆明理工大学理学院,云南昆明650500 [2]昆明理工大学应用统计学研究中心,云南昆明650500

出　　处：《高校应用数学学报（A辑）》2024年第2期141-151,共11页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(12261051);昆明理工大学哲学社会科学科研创新团队(CXTD20230050);昆明理工大学学术科技创新基金(2022KJ150)。

摘　　要：经典的多元线性回归模型要求残差满足高斯-马尔柯夫假设(G-M),在实际生活中由于数据的随机性往往很难满足这个条件.利用Sahu等在2003年提出的偏正态分布来拓展经典的回归模型,给出了偏正态分布众数的近似表达式,建立了偏正态分布下均值和众数多元线性回归模型.在求解模型的参数估计时使用偏正态分布的分层表示构造EM算法.在M步统一给出两点步长梯度下降算法,同时也对均值模型给出显示迭代表达式.最后通过模拟分析以及实例来讨论两种回归模型的可行性.The classic multivariate linear regression model requires the residuals to meet the Gauss-Markov Conditions(G-M),which is often difficult to meet in real life due to the randomness of the data.Using the skew-normal distribution proposed by Sahu in 2003 to expand the classical regression model,the approximate expression of the mode is given under the skew-normal distribution,and the multivariate linear regression models of the mean and mode are established under the skew-normal distribution.In order to estimate the unknown parameters of the model,the EM algorithm is constructed by using the hierarchical representation of the skew-normal distribution.The two-point step gradient descent algorithm is uniformly given in M step,and the explicit iteration expression is also given for the mean regression model.Finally,the feasibility of the two regression models is discussed through simulation studies and examples analysis.

关 键 词：偏正态分布 众数回归模型 均值回归模型 高斯-马尔柯夫假设 EM算法 

分 类 号：O212.1[理学—概率论与数理统计]