SEMIPARAMETRIC ESTIMATION OF PARTIALLY LINEAR TRANSFORMATION MODELS UNDER CONDITIONAL QUANTILE RESTRICTION

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.