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

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.