高维混合效应模型的双正则化分位回归方法研究

发布时间：2018-08-01 11:00

【摘要】：针对高维混合效应模型,本文提出了一种双正则化分位回归方法。通过对随机和固定效应系数同时实施L1正则化惩罚,一方面能够对重要解释变量进行挑选,另一方面能够消除个体随机波动带来的偏差。求解参数估计的交替迭代算法不仅破解了要同时确定两个调整参数的难题,而且算法速度快。模拟结果也表明该方法不仅对误差类型有很强的抗干扰能力,同时在模型有不同稀疏程度时均表现良好,尤其是对于解释变量多于样本的高维情况。为了方便在实际问题中选择最优正则化参数,本文还对两种参数选取标准进行了比较研究。最后利用新方法对一个教育方面的数据进行了实证演示,找出了在各个分位点处对学生成绩有影响的重要因素。
[Abstract]:In this paper, a double regularization quantile regression method is proposed for high dimensional mixed effect model. By simultaneously implementing L1 regularization punishment for both random and fixed effect coefficients, we can select important explanatory variables on the one hand, and eliminate the deviation caused by individual random fluctuations on the other. The alternative iterative algorithm for parameter estimation not only solves the problem of determining two parameters simultaneously, but also has a fast speed. The simulation results also show that this method not only has strong anti-interference ability to the error types, but also performs well when the model has different sparse degree, especially in the case of higher dimension of explanatory variables than samples. In order to facilitate the selection of optimal regularization parameters in practical problems, this paper also makes a comparative study of the two parameters selection criteria. Finally, an empirical demonstration of an educational data is made by using a new method to find out the important factors that affect the students' achievement at each locus.
【作者单位】：湖北工业大学理学院;中国人民大学统计学院;华中师范大学数学与统计学学院;
【基金】：国家社会科学基金项目“高维复杂面板数据的双惩罚分位回归建模方法研究”(17BJY210) 国家自然科学基金项目“基于当代分位回归与鞍点逼近方法的复杂数据分析”(11271368) 教育部人文社会科学青年基金项目“面板数据的分位回归方法及其变量选择问题研究”(13YJC790105) 湖北工科研启业大学博士动基金项目“高维复杂纵向数据的分位回归建模研究”(BSQD13050)资助
【分类号】：C81

【参考文献】