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CONFIDENCE BANDS IN QUANTILE REGRESSION

Published online by Cambridge University Press:  04 November 2009

Wolfgang K. Härdle  and
Song Song
Wolfgang K. Härdle
Affiliation:
Humboldt-Universität zu Berlin
Song Song*
Affiliation:
Humboldt-Universität zu Berlin
*
*Address correspondence to Song Song, Institute for Statistics and Econometrics, Humboldt-Universität zu Berlin, Spandauer Straße 1, 10178 Berlin, Germany; e-mail: songsong@cms.hu-berlin.de.
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Abstract

Let (X1, Y1), …, (Xn, Yn) be independent and identically distributed random variables and let l(x) be the unknown p-quantile regression curve of Y conditional on X. A quantile smoother ln(x) is a localized, nonlinear estimator of l(x). The strong uniform consistency rate is established under general conditions. In many applications it is necessary to know the stochastic fluctuation of the process {ln(x) – l(x)}. Using strong approximations of the empirical process and extreme value theory, we consider the asymptotic maximal deviation sup0≤x≤1 |ln(x) − l(x)|. The derived result helps in the construction of a uniform confidence band for the quantile curve l(x). This confidence band can be applied as a econometric model check. An economic application considers the relation between age and earnings in the labor market by means of parametric model specification tests, which presents a new framework to describe trends in the entire wage distribution in a parsimonious way.

Type
ARTICLES
Information
Econometric Theory , Volume 26 , Issue 4 , August 2010 , pp. 1180 - 1200
Copyright
Copyright © Cambridge University Press 2009

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