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A SINGLE-INDEX QUANTILE REGRESSION MODEL AND ITSESTIMATION

Published online by Cambridge University Press:  14 March 2012

Efang Kong  and
Yingcun Xia
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Abstract

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Models with single-index structures are among the many existing popularsemiparametric approaches for either the conditional mean or the conditionalvariance. This paper focuses on a single-index model for the conditionalquantile. We propose an adaptive estimation procedure and an iterativealgorithm which, under mild regularity conditions, is proved to convergewith probability 1. The resulted estimator of the single-index parametricvector is root-n consistent, asymptotically normal, andbased on simulation study, is more efficient than the average derivativemethod in Chaudhuri, Doksum, and Samarov (1997, Annals of Statistics 19, 760–777). Theestimator of the link function converges at the usual rate for nonparametricestimation of a univariate function. As an empirical study, we apply thesingle-index quantile regression model to Boston housing data. Byconsidering different levels of quantile, we explore how the covariates, ofeither social or environmental nature, could have different effects onindividuals targeting the low, the median, and the high end of the housingmarket.

Information

Type
Research Article
Information
Econometric Theory , Volume 28 , Issue 4 , August 2012 , pp. 730 - 768
Copyright
Copyright © Cambridge University Press 2012

Footnotes

Xia’s research is partially supported by the National Natural Science Foundation of China (11071113) and a research grant from RMI, National University of Singapore.

References

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