Nonparametric Estimation of a Truncated Regression Model with an Application to GATE Program

In this paper we consider identification and estimation of a nonparametric location scale model. We first use the truncated data. Then we use truncated regression model. Truncated regression is used to model dependent variables for which some of the observations are not included in the analysis because of the value of the dependent variable. In the latter case we propose a simple estimation procedure based on combining conditional quantile estimators for three distinct quantiles. The new estimator is shown to converge at the optimal nonparametric rate with a limiting normal distribution. A small scale simulation study indicates that the proposed estimation procedure performs well in finite samples. We also present an empirical application on GATE Program using example data test.