Smoothed Empirical Likelihood Methods for Quantile Regression Models

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Smoothed Empirical Likelihood Methods for Quantile Regression Models

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Yoon-Jae Whang (Korea University)

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Yoon-Jae Whang

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).

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Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1453.

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Length: 44 pages
Date of creation: Mar 2004
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Handle: RePEc:cwl:cwldpp:1453

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Article
- Whang, Yoon-Jae, 2006. "Smoothed Empirical Likelihood Methods For Quantile Regression Models," Econometric Theory, Cambridge University Press, vol. 22(02), pages 173-205, April. [Downloadable!]
Paper
- Yoon-Jae Whang, 2003. "Smoothed Empirical Likelihood Methods for Quantile Regression Models," Econometrics 0310005, EconWPA. [Downloadable!]

Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods

This paper has been announced in the following NEP Reports:

NEP-ALL-2004-06-27 (All new papers)
NEP-ECM-2004-03-14 (Econometrics)

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

repec:cup:etheor:v:11:y:1995:i:1:p:105-21 is not listed on IDEAS
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Other versions:
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Other versions:
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Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January. [Downloadable!] (restricted)
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Other versions:
- Guggenberger, Patrik & Smith, Richard J., 2005. "Generalized Empirical Likelihood Estimators And Tests Under Partial, Weak, And Strong Identification," Econometric Theory, Cambridge University Press, vol. 21(04), pages 667-709, August. [Downloadable!]
Guido W. Imbens & Richard H. Spady & Phillip Johnson, 1998. "Information Theoretic Approaches to Inference in Moment Condition Models," Econometrica, Econometric Society, vol. 66(2), pages 333-358, March.
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- Imbens, G.W. & Johnson, P. & Spady, R.H., 1995. "Information Theoretic Approaches to Inference in Movement Condition Models," Economics Papers 99, Economics Group, Nuffield College, University of Oxford.
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- Guido W. Imbens & Phillip Johnson & Richard H. Spady, 1995. "Information Theoretic Approaches to Inference in Moment Condition Models," NBER Technical Working Papers 0186, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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Hall, Peter & Horowitz, Joel L., 1990. "Bandwidth Selection in Semiparametric Estimation of Censored Linear Regression Models," Econometric Theory, Cambridge University Press, vol. 6(02), pages 123-150, June. [Downloadable!]
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Liangjun Su & Halbert White, 2004. "Testing Conditional Independence Via Empirical Likelihood," University of California at San Diego, Economics Working Paper Series 2003-14, Department of Economics, UC San Diego. [Downloadable!]
Buchinsky, Moshe, 1995. "Estimating the asymptotic covariance matrix for quantile regression models a Monte Carlo study," Journal of Econometrics, Elsevier, vol. 68(2), pages 303-338, August. [Downloadable!] (restricted)
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Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

Paulo Parente & Richard Smith, 2008. "GEL methods for non-smooth moment indicators," CeMMAP working papers CWP19/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
Giuseppe Ragusa, 2008. "Minimum Divergence, Generalized Empirical Likelihoods, and Higher Order Expansions," Working Papers 080906, University of California-Irvine, Department of Economics. [Downloadable!]

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