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SEMIPARAMETRIC ESTIMATION OF PARTIALLY LINEAR TRANSFORMATION MODELS UNDER CONDITIONAL QUANTILE RESTRICTION

Published online by Cambridge University Press:  19 December 2014

Zhengyu Zhang
Zhengyu Zhang*
Affiliation:
Shanghai University of Finance and Economics and Shanghai Academy of Social Sciences
*
*Address correspondence to Zhengyu Zhang, Shanghai University of Finance and Economics, 777, Guoding Road, 200433 Shanghai, China; e-mail: zy.zhang@mail.shufe.edu.cn
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Abstract

This article is concerned with semiparametric estimation of a partially linear transformation model under conditional quantile restriction with no parametric restriction imposed either on the link functional form or on the error term distribution. We describe for the finite-dimensional parameter a $\sqrt n$-consistent estimator which combines the features of Chen (2010)’s maximum integrated score estimator as well as Lee (2003)’s average quantile regression. We show the remaining two infinite-dimensional unknown functions in the model can be separately identified and propose estimators for these functions based on the marginal integration method. Furthermore, a simple approach is proposed to estimate the average partial quantile effect. Two important extensions, i.e., random censoring as well as estimating a transformation model with an endogenous regressor are also considered.

Type
ARTICLES
Information
Econometric Theory , Volume 32 , Issue 2 , April 2016 , pp. 458 - 497
Copyright
Copyright © Cambridge University Press 2014 

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