B0890
Title: Asymptotic normality of quantile regression with generated variables
Authors: Jayeeta Bhattacharya - University of Southampton (United Kingdom) [presenting]
Abstract: Linear quantile regression models are studied when regressors and/or dependent variables are not directly observed, but estimated in an initial first step and used in the second step quantile regression for estimating the quantile parameters. This general class of generated quantile regression (GQR) covers various statistical applications, for instance, the estimation of endogenous quantile regression models and triangular structural equation models, and some new relevant applications are discussed. We study the asymptotic distribution of the two-step estimator, which is challenging because of the presence of generated covariates and/or dependent variable in the non-smooth quantile regression estimator. We employ techniques from empirical process theory to find uniform Bahadur expansion for the two-step estimator, which is used to establish its functional central limit theorem. We illustrate the performance of the GQR estimator through simulations and an empirical application
