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UNIFORM BAHADUR REPRESENTATION FOR NONPARAMETRIC CENSORED QUANTILE REGRESSION: A REDISTRIBUTION-OF-MASS APPROACH

Published online by Cambridge University Press:  15 February 2016

Efang Kong and
Yingcun Xia
Efang Kong*
Affiliation:
University of Electronic Science and TechnologyUniversity of Kent at Canterbury
Yingcun Xia
Affiliation:
University of Electronic Science and TechnologyNational University of Singapore
*
*Address correspondence to Efang Kong, School of Mathematics, Statistics and Actuarial Science, University of Kent at Canterbury, UK; e-mail: e.kong@kent.ac.uk.
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Abstract

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Censored quantile regressions have received a great deal of attention in the literature. In a linear setup, recent research has found that an estimator based on the idea of “redistribution-of-mass” in Efron (1967, Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 4, pp. 831–853, University of California Press) has better numerical performance than other available methods. In this paper, this idea is combined with the local polynomial kernel smoothing for nonparametric quantile regression of censored data. We derive the uniform Bahadur representation for the estimator and, more importantly, give theoretical justification for its improved efficiency over existing estimation methods. We include an example to illustrate the usefulness of such a uniform representation in the context of sufficient dimension reduction in regression analysis. Finally, simulations are used to investigate the finite sample performance of the new estimator.

Information

Type
MISCELLANEA
Information
Econometric Theory , Volume 33 , Issue 1 , February 2017, pp. 242 - 261
Copyright
Copyright © Cambridge University Press 2016 

Footnotes

The authors thank a Co-Editor, an Associate Editor and two referees for their thoughtful comments, and Dr Patrick Saart for his suggestions. Xia’s research is partially supported by National Natural Science Foundation of China (71371095) and a research grant from the Ministry of Education, Singapore (MOE 2014-T2-1-072).

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