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Efficient Estimation of an Additive Quantile Regression

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  • Yebin Cheng

    (Shanghai University of Finance)

  • Jan G. De Gooijer

    (University of Amsterdam)

  • Dawit Zerom

    (California State University at Fullerton)

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). By making use of an internally normalized kernel smoother, the proposed estimator reduces the computational requirement of the latter by the order of the sample size. The second estimator involves sequential fitting by univariate local polynomial quantile regressions for each additive component with the other additive components replaced by the corresponding estimates from the first estimator. The purpose of the extra local averaging is to reduce the variance of the first estimator. We show that 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 using administrative data for the city of Calgary.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 09-104/4.

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Date of creation: 19 Nov 2009
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Handle: RePEc:dgr:uvatin:20090104

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Web page: http://www.tinbergen.nl

Related research

Keywords: Additive models; Asymptotic properties; Dependent data; Internalized kernel smoother; Local polynomial; Oracle efficiency;

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  1. 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.
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