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Smoothed Empirical Likelihood Methods for Quantile Regression Models

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  • Yoon-Jae Whang

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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File URL: http://128.118.178.162/eps/em/papers/0310/0310005.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Econometrics with number 0310005.

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

Note: Type of Document - pdf; prepared on winXP; pages: 32; figures: 2
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Web page: http://128.118.178.162

Related research

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

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References

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  1. 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.
  2. 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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  18. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
  19. repec:cup:etheor:v:11:y:1995:i:1:p:105-21 is not listed on IDEAS
  20. 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.
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Citations

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Cited by:
  1. David Kaplan & Yixiao Sun, 2013. "Smoothed Estimating Equations for Instrumental Variables Quantile Regression," Working Papers 1314, Department of Economics, University of Missouri.
  2. Wanrong Liu & Xuewen Lu, 2011. "Empirical likelihood for density-weighted average derivatives," Statistical Papers, Springer, vol. 52(2), pages 391-412, May.
  3. Tang, Cheng Yong & Leng, Chenlei, 2012. "An empirical likelihood approach to quantile regression with auxiliary information," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 29-36.
  4. Escanciano, J.C. & Goh, S.C., 2014. "Specification analysis of linear quantile models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 495-507.
  5. Giuseppe Ragusa, 2008. "Minimum Divergence, Generalized Empirical Likelihoods, and Higher Order Expansions," Working Papers 080906, University of California-Irvine, Department of Economics.
  6. Escanciano, Juan Carlos & Velasco, Carlos, 2010. "Specification tests of parametric dynamic conditional quantiles," Journal of Econometrics, Elsevier, vol. 159(1), pages 209-221, November.
  7. Otsu, Taisuke, 2008. "Conditional empirical likelihood estimation and inference for quantile regression models," Journal of Econometrics, Elsevier, vol. 142(1), pages 508-538, January.
  8. 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.
  9. Philip Kostov, 2013. "Empirical likelihood estimation of the spatial quantile regression," Journal of Geographical Systems, Springer, vol. 15(1), pages 51-69, January.
  10. Xiaofeng Lv & Rui Li, 2013. "Smoothed empirical likelihood analysis of partially linear quantile regression models with missing response variables," AStA Advances in Statistical Analysis, Springer, vol. 97(4), pages 317-347, October.
  11. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
  12. Pang, Lei & Lu, Wenbin & Wang, Huixia Judy, 2012. "Variance estimation in censored quantile regression via induced smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 785-796.

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