Quantile Regression Using a General Class of Probability Distributions

• Activity Number: 376
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Fassil Nebebe*+ and Tak Mak
• Companies: Concordia University and Concordia University
• Keywords: median regression. ; 'hold-out' sample ; unconstrained optimization

Abstract

It has been established recently that any variable with a continuously differentiable density function is approximately distributed as a linear transformation of a variable from a very general class of probability distribution. Since the class of distribution is conveniently defined through its quantile function, it provides a suitable framework for parametric modeling of median regression. Unlike the traditional approaches using linear programming, quantile regression modeled with the general class of parametric distribution can be managed by the unconstrained optimization of a likelihood function and is considerably simpler. Furthermore, by modeling the scale parameter as a function of the independent variables, this new approach automatically yields any other quantile regression functions without the need of individually modeling and estimating them. In this paper, we examine both the computational and theoretical aspects of this new quantile regression approach. Its efficiencies are compared with those of the traditional quantile regression approaches. We discuss also the use of a "hold-out" sample in testing the fit of the proposed parametric approach.