A fast and efficient implementation of qualitatively constrained quantile smoothing splines: Working paper series--05-08

Exploiting the sparse structure of the design matrices involved in the Frisch-Newton method, we implement a fast and efficient algorithm to compute qualitatively constrained smoothing and regression splines for quantile regression. In a previous implementation (He and Ng, 1999), the linear program involved was solved using the non-simplex active set algorithm for quantile smoothing spines proposed by Ng (1996). The current implementation uses the Frisch-Newton algorithm described in Koenker and Ng (2005a, 2005b). It is a variant of the interiorpoint algorithm proposed by Portnoy and Koenker (1997) which has been shown to outperform the simplex method in many applications. The current 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