Asymptotic Properties of the Location-Scale Regression Estimators for Left Truncated Data

Location Scale Regression for Left Truncated Data

Abstract

We consider the nonparametric estimation of a heteroscedastic regression model Y = m(X)+σ(X)ϵ, where the error term ϵ is independent of the covariate X, and the functions m and σ are unknown. The response variable Y is allowed to be interfered by a left truncation random variable T. In this work, we propose kernel-estimators for both the location and scale functions m and σ and investigate their strong uniform consistency rates as well as their asymptotic normality.  The finite sample performance of the proposed estimator of the regression function m(.) is extensively studied via simulation and indicate that in presence of heteroscedasticity, our new estimator outperforms the classical one (when ignoring heteroscedasticity) and is less sensitive to the presence of outliers. We also investigate the performance of the scale function estimator σ(.). Furthermore, an application to real data demonstrates the effectiveness of our method in terms of prediction accuracy.