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A SINGLE-INDEX QUANTILE REGRESSION MODEL AND ITS ESTIMATION

Published online by Cambridge University Press:  14 March 2012

Efang Kong  and
Yingcun Xia
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Abstract

Models with single-index structures are among the many existing popular semiparametric approaches for either the conditional mean or the conditional variance. This paper focuses on a single-index model for the conditional quantile. We propose an adaptive estimation procedure and an iterative algorithm which, under mild regularity conditions, is proved to converge with probability 1. The resulted estimator of the single-index parametric vector is root-n consistent, asymptotically normal, and based on simulation study, is more efficient than the average derivative method in Chaudhuri, Doksum, and Samarov (1997, Annals of Statistics 19, 760–777). The estimator of the link function converges at the usual rate for nonparametric estimation of a univariate function. As an empirical study, we apply the single-index quantile regression model to Boston housing data. By considering different levels of quantile, we explore how the covariates, of either social or environmental nature, could have different effects on individuals targeting the low, the median, and the high end of the housing market.

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

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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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