Quantile Regression via an MM Algorithm
Quantile Regression via an MM Algorithm
复制标题
DOI：
10.1080/10618600.2000.10474866
复制
发表时间：
2000-03
影响因子：
2.4
通讯作者：
D. Hunter;K. Lange
中科院分区：
文献类型：
--
作者：
D. Hunter;K. Lange
摘要 分位数回归是一种越来越受欢迎的方法，用于在协变量值的条件下估计分布的分位数。回归分位数对异常值的影响具有稳健性，并且一次取多个分位数时，它们比单一的中心估计能更完整地描述条件分布。本文首先提出一种无需排序即可找到样本分位数的迭代算法，然后探讨了该算法对非线性分位数回归的推广。我们的分位数回归算法被称为MM算法，即最大化 - 最小化算法，因为它需要用一个二次函数对目标函数进行最大化，然后对该二次函数进行最小化。该算法在概念上简单且易于编码，我们的数值测试表明，对于大多数问题，它在计算上与最近的一种内点算法具有竞争力。
Abstract Quantile regression is an increasingly popular method for estimating the quantiles of a distribution conditional on the values of covariates. Regression quantiles are robust against the influence of outliers and, taken several at a time, they give a more complete picture of the conditional distribution than a single estimate of the center. This article first presents an iterative algorithm for finding sample quantiles without sorting and then explores a generalization of the algorithm to nonlinear quantile regression. Our quantile regression algorithm is termed an MM, or majorize—minimize, algorithm because it entails majorizing the objective function by a quadratic function followed by minimizing that quadratic. The algorithm is conceptually simple and easy to code, and our numerical tests suggest that it is computationally competitive with a recent interior point algorithm for most problems.