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Smoothed Empirical Likelihood Methods For Quantile Regression Models

  • Whang, Yoon-Jae

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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Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 22 (2006)
Issue (Month): 02 (April)
Pages: 173-205

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Handle: RePEc:cup:etheor:v:22:y:2006:i:02:p:173-205_06
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  1. 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.
  2. Joel L. Horowitz, 1996. "Bootstrap Methods for Median Regression Models," Econometrics 9608004, EconWPA.
  3. repec:cup:etheor:v:6:y:1990:i:2:p:123-50 is not listed on IDEAS
  4. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
  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.
  6. Su, Liangjun & White, Halbert, 2003. "Testing Conditional Independence Via Empirical Likelihood," University of California at San Diego, Economics Working Paper Series qt35v8g0fm, Department of Economics, UC San Diego.
  7. 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.
  8. Francesco Bravo, 2002. "Testing linear restrictions in linear models with empirical likelihood," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 104-130, June.
  9. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
  10. 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.
  11. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  12. Song Xi Chen & Hengjian Cui, 2006. "On Bartlett correction of empirical likelihood in the presence of nuisance parameters," Biometrika, Biometrika Trust, vol. 93(1), pages 215-220, March.
  13. 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.
  14. Karun Adusumilli & Taisuke Otsu, 2014. "Empirical Likelihood for Random Sets," STICERD - Econometrics Paper Series /2014/574, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  15. Song Chen, 1993. "On the accuracy of empirical likelihood confidence regions for linear regression model," Annals of the Institute of Statistical Mathematics, Springer, vol. 45(4), pages 621-637, December.
  16. Chen, Song Xi & Cui, Hengjian, 2007. "On the second-order properties of empirical likelihood with moment restrictions," Journal of Econometrics, Elsevier, vol. 141(2), pages 492-516, December.
  17. 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.
  18. Moshe Buchinsky, 1998. "Recent Advances in Quantile Regression Models: A Practical Guideline for Empirical Research," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 88-126.
  19. Hahn, Jinyong, 1995. "Bootstrapping Quantile Regression Estimators," Econometric Theory, Cambridge University Press, vol. 11(01), pages 105-121, February.
  20. repec:cup:etheor:v:11:y:1995:i:1:p:105-21 is not listed on IDEAS
  21. 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.
  22. Yuichi Kitamura, 2001. "Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions," Econometrica, Econometric Society, vol. 69(6), pages 1661-1672, November.
  23. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
  24. 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.
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