### 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) |
---|---|

Pages (from-to) | 418-440 |

Number of pages | 23 |

Journal | Sankhya: The Indian Journal of Statistics |

Volume | 67 |

Issue number | 2 |

State | Published - 2005 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistics and Probability

### Cite this

*Sankhya: The Indian Journal of Statistics*,

*67*(2), 418-440.

**Inequality constrained quantile regression.** / Koenker, Roger; Ng, Pin T.

Research output: Contribution to journal › Article

*Sankhya: The Indian Journal of Statistics*, vol. 67, no. 2, pp. 418-440.

}

TY - JOUR

T1 - Inequality constrained quantile regression

AU - Koenker, Roger

AU - Ng, Pin T

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

KW - Interior point algorithm

KW - Qualitative constraints

KW - Quantile regression

KW - Smoothing

KW - Sparse matrices

UR - http://www.scopus.com/inward/record.url?scp=27944460394&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=27944460394&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:27944460394

VL - 67

SP - 418

EP - 440

JO - Sankhya: The Indian Journal of Statistics

JF - Sankhya: The Indian Journal of Statistics

SN - 0972-7671

IS - 2

ER -