Quantile Regression via an MM Algorithm

David R. Hunter, Kenneth Lange

Research output: Contribution to journalArticlepeer-review

215 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)60-77
Number of pages18
JournalJournal of Computational and Graphical Statistics
Issue number1
StatePublished - Mar 2000

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Statistics, Probability and Uncertainty


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