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Smoothed Empirical Likelihood Methods for Quantile Regression Models

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Author Info
Yoon-Jae Whang

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Abstract

The standard confidence regions based on the first-order approximation of quantile regression estimators can be inaccurate in small samples. We show 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. Also, from the duality of confidence regions and hypothesis tess, our results imply that the smoothed empirical likelihood confidence regions might 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 EconWPA in its series Econometrics with number 0310005.

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Length: 32 pages
Date of creation: 23 Oct 2003
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Handle: RePEc:wpa:wuwpem:0310005

Note: Type of Document - pdf; prepared on winXP; pages: 32; figures: 2
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Related research
Keywords: Bartlett correction; Bootstrap; Edgeworth expansion; Empirical likelihood; Quantile regression model; Censored quantile regression model;

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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

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References listed on IDEAS
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  1. repec:cup:etheor:v:11:y:1995:i:1:p:105-21 is not listed on IDEAS
  2. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January. [Downloadable!] (restricted)
  3. Horowitz, Joel L., 2001. "The Bootstrap," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 52, pages 3159-3228 Elsevier. [Downloadable!] (restricted)
  4. Joel L. Horowitz, 1998. "Bootstrap Methods for Median Regression Models," Econometrica, Econometric Society, vol. 66(6), pages 1327-1352, November.
    Other versions:
  5. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, 01. [Downloadable!] (restricted)
    Other versions:
  6. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January. [Downloadable!] (restricted)
  7. Patrik Buggenberger & Richard Smith, 2003. "Generalized empirical likelihood estimators and tests under partial, weak and strong identification," CeMMAP working papers CWP08/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
    Other versions:
  8. 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.
    Other versions:
  9. 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!]
  10. Bravo, Francesco, 2004. "Empirical Likelihood Based Inference With Applications To Some Econometric Models," Econometric Theory, Cambridge University Press, vol. 20(02), pages 231-264, April. [Downloadable!]
  11. repec:cup:etheor:v:6:y:1990:i:2:p:123-50 is not listed on IDEAS
  12. 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!]
  13. 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)
  14. Yuichi Kitamura, 2001. "Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions," Econometrica, Econometric Society, vol. 69(6), pages 1661-1672, November. [Downloadable!] (restricted)
  15. Hahn, Jinyong, 1995. "Bootstrapping Quantile Regression Estimators," Econometric Theory, Cambridge University Press, vol. 11(01), pages 105-121, February. [Downloadable!]
  16. Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2003. "Empirical likelihood estimation and consistent tests with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 117(1), pages 55-93, November. [Downloadable!] (restricted)
  17. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July. [Downloadable!] (restricted)
  18. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June. [Downloadable!] (restricted)
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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.)

  1. 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!]
  2. 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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