Smoothed Empirical Likelihood Methods for Quantile Regression Models

45 Pages Posted: 24 Mar 2004

See all articles by Yoon-Jae Whang

Yoon-Jae Whang

Seoul National University - School of Economics

Date Written: March 2004

Abstract

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).

Keywords: Bartlett correction, Bootstrap, Edgeworth expansion, Empirical likelihood, Quantile regression model, Censored quantile regression model

JEL Classification: C12, C13, C15

Suggested Citation

Whang, Yoon-Jae, Smoothed Empirical Likelihood Methods for Quantile Regression Models (March 2004). Cowles Foundation Discussion Paper No. 1453, Available at SSRN: https://ssrn.com/abstract=520883

Yoon-Jae Whang (Contact Author)

Seoul National University - School of Economics ( email )

San 56-1, Silim-dong, Kwanak-ku
Seoul 151-742
Korea
+82 2 80 6362 (Phone)
+82 2 86 4231 (Fax)

HOME PAGE: http://plaza.snu.ac.kr/~whang

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