近年来, 关于部分线性分位回归模型的估计方法的研究得到了较多的关注. 但由于目标函数的非光滑性, 估计程序的实现是比较具有挑战性的. 文章将采用MM (Majorization Minimization) 算法计算部分线性分位数回归模型的估计. 其基本原理是首先找到目标函数的优化函数, 然后借助优化函数的最小化过程, 逐步迭代至目标函数的解. 数值模拟和实证研究表明该算法具有较好的稳定性和较强的数值计算能力.

The estimation of the partial linear quantile regression model has obtained much attention in recent years. However, the realizations of the estimating methods are very challenging since the objective functions are non-smooth. In this paper, we employ the MM (Majorization Minimization) algorithm to calculate the estimators of the regression coefficient of the partial linear quantile regression model. This algorithm first finds surrogate functions that minimize the objective functions. Then via optimizing the surrogate function, the solutions can be obtained which minimize the objective functions. To validate the performance of the proposed algorithm, extensive simulation studies are conducted. It is shown that the proposed algorithm is robust and computationally competitive with the common-used interior algorithm.