Quantile Regression via an MM Algorithm

David R. Hunter, Kenneth Lange
2000 Journal of Computational And Graphical Statistics  
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. The current paper first presents an iterative algorithm for finding sample quantiles without sorting and then explores a generalization of the algorithm to
more » ... 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.
doi:10.2307/1390613 fatcat:s6sgfipr3zh4bgrskupsx6s5hq