An implementation for regression quantile estimation
by
Thomas W. Yee
University of Auckland

There are a number of methods that have been developed for quantile regression. This paper will overview several methods, and focus on the LMS method (Cole and Green, 1992), which is a flexible method based on splines. The basic idea is that, for a fixed value of the covariate, a Box-Cox transformation of the response is applied to obtain standard normality. The three parameters are chosen to maximize a penalized log-likelihood, which amounts to spline smoothing. One unpublished extension by Lopatatzidis and Green is to transform to a gamma distribution-this helps overcome a range-restriction problem in the original formulation. In this paper a new method is proposed based on the Yeo and Johnson (2000) transformation. It has the advantage that it allows for both positive and negative values in the response. R/SPLUS software written by the author implementing the LMS method and variants are described and illustrated with data from a New Zealand cross-section workforce study.

Date received: May 26, 2002