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Nonparametric Estimation of an Additive Quantile Regression Model

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  • Horowitz, Joel L.
  • Lee, Sokbae

Abstract

This paper is concerned with estimating the additive components of a nonparametric additive quantile regression model. We develop an estimator that is asymptotically normally distributed with a rate of convergence in probability of $n^{-r/(2r+1)}$ when the additive components are $r$-times continuously differentiable for some $r \geq 2$. This result holds regardless of the dimension of the covariates and, therefore, the new estimator has no curse of dimensionality. In addition, the estimator has an oracle property and is easily extended to a generalized additive quantile regression model with a link function. The numerical performance and usefulness of the estimator are illustrated by Monte Carlo experiments and an empirical example

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Bibliographic Info

Article provided by American Statistical Association in its journal Journal of the American Statistical Association.

Volume (Year): 100 (2005)
Issue (Month): (December)
Pages: 1238-1249

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Handle: RePEc:bes:jnlasa:v:100:y:2005:p:1238-1249

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References

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  1. Lee, Sokbae, 2003. "Efficient Semiparametric Estimation Of A Partially Linear Quantile Regression Model," Econometric Theory, Cambridge University Press, vol. 19(01), pages 1-31, February.
  2. Gozalo, Pedro L. & Linton, Oliver B., 2001. "Testing additivity in generalized nonparametric regression models with estimated parameters," Journal of Econometrics, Elsevier, vol. 104(1), pages 1-48, August.
  3. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339 Elsevier.
  4. De Gooijer J.G. & Zerom D., 2003. "On Additive Conditional Quantiles With High Dimensional Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 135-146, January.
  5. Joel L. Horowitz & N. E. Savin, 2001. "Binary Response Models: Logits, Probits and Semiparametrics," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 43-56, Fall.
  6. Khan, Shakeeb, 2001. "Two-stage rank estimation of quantile index models," Journal of Econometrics, Elsevier, vol. 100(2), pages 319-355, February.
  7. Joel Horowitz & Enno Mammen, 2002. "Nonparametric estimation of an additive model with a link function," CeMMAP working papers CWP19/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  8. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July.
  9. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
  10. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November.
  11. repec:wop:humbsf:2002-63 is not listed on IDEAS
  12. Yishay Yafeh & Oved Yosha, 2003. "Large Shareholders and Banks: Who Monitors and How?," Economic Journal, Royal Economic Society, vol. 113(484), pages 128-146, January.
  13. Doksum, Kjell & Koo, Ja-Yong, 2000. "On spline estimators and prediction intervals in nonparametric regression," Computational Statistics & Data Analysis, Elsevier, vol. 35(1), pages 67-82, November.
  14. Horowitz, Joel L. & Mammen, Enno, 2002. "Nonparametric estimation of an additive model with a link function," SFB 373 Discussion Papers 2002,63, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  15. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  16. He, Xuming & Shi, Peide, 1996. "Bivariate Tensor-Product B-Splines in a Partly Linear Model," Journal of Multivariate Analysis, Elsevier, vol. 58(2), pages 162-181, August.
  17. Horowitz, Joel L., 1993. "Semiparametric estimation of a work-trip mode choice model," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 49-70, July.
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Citations

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Cited by:
  1. Wolfgang Karl Härdle & Ya'acov Ritov & Weining Wang, 2013. "Tie the straps: uniform bootstrap confidence bands for bounded influence curve estimators," SFB 649 Discussion Papers SFB649DP2013-047, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. Efang Kong & Oliver Linton & Yingcun Xia, 2009. "Uniform Bahadur Representation for LocalPolynomial Estimates of M-Regressionand Its Application to The Additive Model," STICERD - Econometrics Paper Series /2009/535, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  3. repec:wyi:wpaper:002008 is not listed on IDEAS
  4. Ichimura, Hidehiko & Todd, Petra E., 2007. "Implementing Nonparametric and Semiparametric Estimators," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 74 Elsevier.
  5. repec:wyi:wpaper:001957 is not listed on IDEAS
  6. Cai, Zongwu & Xiao, Zhijie, 2012. "Semiparametric quantile regression estimation in dynamic models with partially varying coefficients," Journal of Econometrics, Elsevier, vol. 167(2), pages 413-425.
  7. Wu, Tracy Z. & Yu, Keming & Yu, Yan, 2010. "Single-index quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1607-1621, August.
  8. repec:wyi:journl:002112 is not listed on IDEAS
  9. repec:wyi:journl:002094 is not listed on IDEAS
  10. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
  11. Holger Dette, 2013. "Comments on: An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 22(3), pages 437-441, September.
  12. Lian, Heng, 2012. "A note on the consistency of Schwarz’s criterion in linear quantile regression with the SCAD penalty," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1224-1228.
  13. Cheng, Yebin & De Gooijer, Jan & Zerom, Dawit, 2009. "Efficient Estimation of an Additive Quantile Regression Model," MPRA Paper 14388, University Library of Munich, Germany.
  14. Yebin Cheng & Jan G. De Gooijer & Dawit Zerom, 2009. "Efficient Estimation of an Additive Quantile Regression," Tinbergen Institute Discussion Papers 09-104/4, Tinbergen Institute.
  15. repec:wyi:journl:002114 is not listed on IDEAS
  16. Holger Dette & Regine Scheder, 2011. "Estimation of additive quantile regression," Annals of the Institute of Statistical Mathematics, Springer, vol. 63(2), pages 245-265, April.
  17. Yue, Yu Ryan & Rue, Håvard, 2011. "Bayesian inference for additive mixed quantile regression models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 84-96, January.

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