带缺失数据的偏正态众数回归模型的参数估计

Parameter estimation of skew-normal mode regression model with missing data

针对现实生活中大量数据存在偏斜的情况,构建偏正态数据下的众数回归模型.又加之数据的缺失常有发生,采用插补方法处理缺失数据集,为比较插补效果,考虑对响应变量随机缺失情形进行统计推断研究.利用高斯牛顿迭代法给出众数回归模型参数的极大似然估计,比较该模型在均值插补,回归插补,众数插补三种插补条件下的插补效果.随机模拟和实例分析的研究结果表明,众数回归模型优于传统的均值回归模型.众数插补与另外两种插补方法相比,在带有缺失的偏正态数据下表现出了对众数回归模型参数估计的可行性.

Large amounts of data are skewed in real life, the mode regression model is proposed based on skew-normal distribution. In addition, the missing of data often occurs, and interpolation method is adopted to deal with the missing data set. In order to compare the effect of interpolation,make statistical study based on the random missing of response variables. In this paper, the maximum likelihood estimation of mode regression model parameters is given by using Gaussian-Newton iterative algorithm, and the interpolation effects of the model are compared under three interpolation conditions: mean interpolation, regression interpolation and mode interpolation. The results of simulation and a real data example show that the mode regression model is better than the traditional mean regression model under skew-normal data. Compared with the other two interpolation methods, mode interpolation shows the feasibility of the parameter estimation of mode regression model in the missing of skew-normal data.