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Smoothed Empirical Likelihood Methods For Quantile Regression Models

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  • Whang, Yoon-Jae

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 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 errors of order n 2, where n denotes the sample size. Our result is an extension of the previous result of Chen and Hall (1993, Annals of Statistics 21, 1166 1181) to the regression context. 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, Econometrica 66, 1327 1351).I thank the co-editor Bruce Hansen and anonymous referees for valuable suggestions and comments. I also thank Song X. Chen, Joel Horowitz, Yuichi Kitamura, Oliver Linton, Whitney Newey, Peter Phillips, and Richard Smith for helpful comments. Parts of this paper were written while I was visiting the Cowles Foundation at Yale University, whose hospitality is gratefully acknowledged. Young-Hyun Cho has provided excellent research assistance. This work was supported by the Korea Research Foundation grant KRF 2003-041-B00072.

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Bibliographic Info

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. 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.
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  7. 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.
  8. Joel L. Horowitz, 1998. "Bootstrap Methods for Median Regression Models," Econometrica, Econometric Society, vol. 66(6), pages 1327-1352, November.
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Cited by:
  1. 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.
  2. 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.
  3. Giuseppe Ragusa, 2011. "Minimum Divergence, Generalized Empirical Likelihoods, and Higher Order Expansions," Econometric Reviews, Taylor & Francis Journals, vol. 30(4), pages 406-456.
  4. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
  5. 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.
  6. Juan Carlos Escanciano & Carlos Velasco, 2008. "Specification Tests of Parametric Dynamic Conditional Quantiles," Caepr Working Papers 2008-021, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
  7. Philip Kostov, 2013. "Empirical likelihood estimation of the spatial quantile regression," Journal of Geographical Systems, Springer, vol. 15(1), pages 51-69, January.
  8. Wanrong Liu & Xuewen Lu, 2011. "Empirical likelihood for density-weighted average derivatives," Statistical Papers, Springer, vol. 52(2), pages 391-412, May.
  9. Kaplan, David M. & Sun, Yixiao, 2012. "Smoothed Estimating Equations For Instrumental Variables Quantile Regression," University of California at San Diego, Economics Working Paper Series qt888657tp, Department of Economics, UC San Diego.
  10. Escanciano, J.C. & Goh, S.C., 2014. "Specification analysis of linear quantile models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 495-507.
  11. Parente, Paulo M.D.C. & Smith, Richard J., 2011. "Gel Methods For Nonsmooth Moment Indicators," Econometric Theory, Cambridge University Press, vol. 27(01), pages 74-113, February.
  12. Otsu, Taisuke, 2008. "Conditional empirical likelihood estimation and inference for quantile regression models," Journal of Econometrics, Elsevier, vol. 142(1), pages 508-538, January.

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