**Sankhya:
The Indian Journal of Statistics**

2005, Volume 67, Pt. 2, 418--440

**Inequality Constrained Quantile
Regression**

By

Roger Koenker, University of Illinois
at Urbana-Champaign, USA

Pin Ng, University of Northern Arizona, Flagstaff, USA

SUMMARY. 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..

*AMS (1991) subject classification. *Primary 62J05, 90C05, 65D10; Secondary
62G08, 90C06, 65F50, 62G35.

*Key words and phrases. *Quantile regression, qualitative constraints,
interior point algorithm, sparse matrices, smoothing.