纵向数据分位回归模型的降维算法模拟研究

Simulation Studies on Dimension Reduction Algorithm for Quantile Regression Model of Longitudinal Data

文章对含多重随机效应的纵向数据模型提出了两种新的惩罚分位回归法,通过对分位回归系数分别施加Lasso和自适应Lasso惩罚,两种方法能够对模型中的自变量进行自动选择。并设计了参数估计的交替迭代算法,讨论了最优惩罚参数选取方法。蒙特卡罗模拟结果显示,新方法不仅能对分位回归系数做出准确的估计和选择,而且对随机误差分布也具有较强的稳健性。

This paper proposes two new penalized quantile regression methods for the longitudinal data model with multiple random effects. By applying Lasso and adaptive Lasso penalties to the quantile regression coefficients, both methods can be used to automatically select the independent variables in the model. The paper also designs the iterative algorithm for parameter estimation and discusses the optimal penalty parameter selection method. The results of Monte Carlo simulation studies show that the two new methods can not only estimate and select the quantile regression coefficient precisely, but also have strong robustness of the random error distribution.