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Nonparametric Estimation of an Additive Quantile Regression Model

  • Horowitz, Joel L.
  • Lee, Sokbae

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 = 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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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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  1. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. HÄRDLE, Wolfgang, 1992. "Applied nonparametric methods," CORE Discussion Papers 1992003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  8. 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.
  9. 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.
  10. Khan, Shakeeb, 2001. "Two-stage rank estimation of quantile index models," Journal of Econometrics, Elsevier, vol. 100(2), pages 319-355, February.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. Oliver LINTON, . "Applied nonparametric methods," Statistic und Oekonometrie 9312, Humboldt Universitaet Berlin.
  16. 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.
  17. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
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