混合效应模型的双MCP惩罚分位回归研究

针对混合效应模型，在已有的双Lasso正则化分位回归(DLQR)的基础上，结合MCP惩罚，提出了双MCP正则化分位回归(DMQR).通过对惩罚方法的改进，使得模型的拟合效果大大提高.在求解参数时使用交替迭代算法使得每次只用求解单个MCP惩罚的分位回归，并结合针对非凸惩罚的迭代坐标下降法(QICD)使得计算的速度大大提高.在稀疏模型的模拟研究中发现，无论在何种误差条件下，DMQR都能很好的排除冗余变量，效果相对于DLQR有了较大的提升.且在模型的稀疏程度不同时，都能得到很好的模拟结果.

Research on double MCP penalty quantile regression based on mixed effects model

Aiming at the mixed effects model， based on the existing double Lasso regularized quantile regression (DLQR)， combined with the MCP penalty， a double MCP regularized quantile regression (DMQR) is proposed. Through the improvement of the penalty method， the fitting effect of the model is greatly improved. When solving the parameters， the alternate iterative algorithm is used to solve the quantile regression of a single MCP penalty each time， and combined with the iterative coordinate descent method (QICD) for non-convex penalty， the calculation speed is greatly improved. In the simulation study of the sparse model， it is found that no matter what the error conditions， DMQR eliminates redundant variables very well， and the effect has been greatly improved compared with DLQR. And when the sparseness of the model is different， good simulation results would be obtained.