A fast and efficient implementation of qualitatively constrained quantile smoothing splines

We implement a fast and efficient algorithm to compute qualitatively constrained smoothing and regression splines for quantile regression, exploiting the sparse structure of the design matrices involved in the method. In a previous implementation, the linear program involved was solved using a simplex-like algorithm for quantile smoothing splines. The current implementation uses the Frisch-Newton algorithm, recently described by Koenker and Ng (2005b). It is a variant of the interior-point algorithm proposed by Portnoy and Koenker (1997), which has been shown to outperform the simplex method in many applications. The current R implementation relies on the R package SparseM of Koenker and Ng (2003) which contains a collection of basic linear algebra routines for sparse matrices to exploit the sparse structure of the matrices involved in the linear program to further speed up computation and save memory usage. A small simulation illustrates the superior performance of the new implementation.