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Smoothed Empirical Likelihood Methods For Quantile Regression Models, Yoon-Jae Whang

Cowles Foundation Discussion Papers

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. …