JSM 2005 - Toronto

Abstract #303707

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 401
Type: Contributed
Date/Time: Wednesday, August 10, 2005 : 10:30 AM to 12:20 PM
Sponsor: General Methodology
Abstract - #303707
Title: Nonstandard Asymptotics for Quantile Regression
Author(s): Chuan Goh*+
Companies: University of Toronto
Address: Department of Economics, Toronto, ON, M5S 3G7, Canada
Keywords: quantile regression ; location-scale model ; hypothesis testing ; bandwidth selection ; generalized functions
Abstract:

In this paper, I propose a new asymptotic distributional approximation for symmetric t-tests in the context of linear quantile regression models. Unlike the usual first-order Gaussian approximation, the new distributional approximation depends explicitly on the bandwidth used to implement a nonparametric estimator of the asymptotic variance parameter, which is assumed to be of the difference quotient type suggested by Hendricks and Koenker (1992). Unlike the conventional Gaussian first-order approximation, the new asymptotics proposed in this paper is predicated explicitly on inconsistent estimation of the asymptotic variance parameter. Critical values for testing are now functions of the amount of smoothing involved in constructing estimates of the asymptotic variance, and practitioners are therefore afforded explicit guidance on how much smoothing is appropriate. Numerical evidence presented in this paper indicates the new asymptotics implies a range of bandwidths that produce tests with good size properties and high power against local alternatives, particularly in the case of models exhibiting no more than a mild degree of heteroskedasticity.

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