Quantile regression is a robust and practically useful way to efficiently model quantile varying correlation and predict varied response quantiles of interest. This article constructs and tests MM algorithms, which are simple to code and have been suggested superior to some other prominent quantile regression methods in nonregularized problems, in an array of quantile regression settings including linear (modeling different quantile coefficients both separately and simultaneously), nonparametric, regularized, and monotone quantile regression. Applications to various real data sets and two simulation studies comparing MM to existing tested methods have corroborated our algorithms' effectiveness. We have made one key advance by generalizing our MM algorithm to efficiently fit easy-to-predict-and-interpret parametric quantile regression models for data sets exhibiting manifest complicated nonlinear correlation patterns, which has not yet been covered by current literature to the best of our knowledge.

翻译：分位数回归是一种稳健且实用的方法，能够有效建模分位数变化的相关性并预测感兴趣的不同响应分位数。本文构建并测试了MM算法，该算法编码简单，在非正则化问题中已被认为优于其他一些著名的分位数回归方法。我们在一系列分位数回归场景中进行了验证，包括线性（分别和同时建模不同分位数系数）、非参数、正则化及单调分位数回归。通过多个真实数据集的应用以及两项将MM算法与现有测试方法进行比较的模拟研究，均证实了我们算法的有效性。我们取得了一项关键进展：将MM算法推广至能够高效拟合易于预测和解释的参数化分位数回归模型，适用于呈现明显复杂非线性相关模式的数据集——据我们所知，当前文献尚未涵盖这一方向。