COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1453 Smoothed Empirical Likelihood Methods for Quantile Regression Models Yoon-Jae Whang March 2004 This paper considers an empirical likelihood method to estimate the parameters of the
quantile regression (QR) models and to construct confidence regions that are accurate in
finite samples. To achieve the higher-order refinements, we smooth the estimating
equations for the empirical likelihood. We show that the smoothed empirical likelihood
(SEL) estimator is first-order asymptotically equivalent to the standard QR estimator and
establish that confidence regions based on the smoothed empirical likelihood ratio have
coverage errors of order n–1 and may be Bartlett-corrected to
produce regions with an error of order n–2, where n denotes
the sample size. We further extend these results to censored quantile regression models.
Our results are extensions of the previous results of Chen and Hall (1993) to the
regression contexts. Monte Carlo experiments suggest that the smoothed empirical
likelihood confidence regions may be more accurate in small samples than the confidence
regions that can be constructed from the smoothed bootstrap method recently suggested by
Horowitz (1998). |
