基于双自适应Lasso惩罚的随机效应分位回归模型研究

研究目标：解决随机效应分位回归模型中固定效应和随机效应系数同时估计和选择问题。研究方法：对固定效应和随机效应系数同时实施自适应Lasso惩罚，并为参数估计设计交替迭代算法。研究发现：新方法不仅对随机误差分布具有较强的稳健性，而且在不同稀疏度模型下均有着良好的表现，尤其是在高维情形时。研究创新：本文提出的方法在对模型中重要自变量进行选择的同时能够充分考虑随机效应的影响；交替迭代算法不仅有效解决了需要选择两个惩罚参数的困境，而且收敛速度快。研究价值：为实际工作者对面板数据和纵向数据的分析提供了有效的建模方法。

The Research of Double Adaptive Lasso Quantile Regression Model with Random Effects

Research Objectives:To solve the problem of selecting important predictive variables and random effects coefficients in quantile regression model with random effects simultaneously.Research Methods:We propose a double adaptive Lasso quantile regression method by applying the adaptive Lasso penalty to the fixed and random effect coefficients,and an iterative algorithm is also designed for parameter estimation.Research Findings:The results show that the new method is not only robust to the random error distribution,but also has good performance even under different sparsity models,especially in the high-dimensional case.Research Innovations:The new method can select the important predictive variables in the random effects model meanwhile fully taking account of the impact of unknown random effects.The iterative algorithm designed for parameter estimation not only solves the dilemma of selecting two regularization parameters,but also converges quickly.Research Value:It provides an effective modeling method for the analysis of panel data and longitudinal data