### Abstract

An algorithm for computing parametric linear quantile regression estimates subject to linear inequality constraints is described. The algorithm is a variant of the interior point algorithm described in Koenker and Portnoy (1997) for unconstrained quantile regression and is consequently quite efficient even for large problems, particularly when the inherent sparsity of the resulting linear algebra is exploited. Applications to qualitatively constrained nonparametric regression are described in the penultimate sections. Implementations of the algorithm are available in MATLAB and R.

Original language | English (US) |
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Pages (from-to) | 418-440 |

Number of pages | 23 |

Journal | Sankhya: The Indian Journal of Statistics |

Volume | 67 |

Issue number | 2 |

State | Published - Nov 30 2005 |

### Keywords

- Interior point algorithm
- Qualitative constraints
- Quantile regression
- Smoothing
- Sparse matrices

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

Koenker, R., & Ng, P. (2005). Inequality constrained quantile regression.

*Sankhya: The Indian Journal of Statistics*,*67*(2), 418-440.