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Efficient Estimation of an Additive Quantile Regression Model

Author

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  • YEBIN CHENG
  • JAN G. DE GOOIJER
  • DAWIT ZEROM

Abstract

In this paper two kernel-based nonparametric estimators are proposed for estimating the components of an additive quantile regression model. The first estimator is a computationally convenient approach which can be viewed as a viable alternative to the method of De Gooijer and Zerom (2003). With the aim to reduce variance of the first estimator, a second estimator is defined via sequential fitting of univariate local polynomial quantile smoothing for each additive component with the other additive components replaced by the corresponding estimates from the first estimator. The second estimator achieves oracle efficiency in the sense that each estimated additive component has the same variance as in the case when all other additive components were known. Asymptotic properties are derived for both estimators under dependent processes that are strictly stationary and absolutely regular. We also provide a demonstrative empirical application of additive quantile models to ambulance travel times.
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Suggested Citation

  • Yebin Cheng & Jan G. De Gooijer & Dawit Zerom, 2011. "Efficient Estimation of an Additive Quantile Regression Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(1), pages 46-62, March.
    • Handle: RePEc:bla:scjsta:v:38:y:2011:i:1:p:46-62
    DOI: j.1467-9469.2010.00706.x
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    References listed on IDEAS

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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(1), pages 1-31, February.
    2. Horowitz, Joel L. & Lee, Sokbae, 2005. "Nonparametric Estimation of an Additive Quantile Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1238-1249, December.
    3. Cai, Zongwu & Xu, Xiaoping, 2009. "Nonparametric Quantile Estimations for Dynamic Smooth Coefficient Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 371-383.
    4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    5. 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.
    6. 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.
    7. Cai, Zongwu & Ould-Saïd, Elias, 2003. "Local M-estimator for nonparametric time series," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 433-449, December.
    8. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, September.
    9. Toshio Honda, 2000. "Nonparametric Estimation of a Conditional Quantile for α-Mixing Processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 459-470, September.
    10. Manzan, Sebastiano & Zerom, Dawit, 2005. "Kernel estimation of a partially linear additive model," Statistics & Probability Letters, Elsevier, vol. 72(4), pages 313-322, May.
    11. Keming Yu & Zudi Lu, 2004. "Local Linear Additive Quantile Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 333-346, September.
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    Cited by:

    1. Noh, Hohsuk & Lee, Eun, 2012. "Component Selection in Additive Quantile Regression Models," LIDAM Discussion Papers ISBA 2012021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. De Gooijer, Jan G. & Zerom, Dawit, 2019. "Semiparametric quantile averaging in the presence of high-dimensional predictors," International Journal of Forecasting, Elsevier, vol. 35(3), pages 891-909.

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    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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