Nonparametric Estimation of the Error Functional of a Location-Scale Model

Abstract

Two estimators of the distribution of the error term are proposed based on nonparametric regression residuals; considering a heteroscadastic location-scale model where the mean and variance functions are smooth, and the error term is independent of the independent variable. The asymptotic properties of the two estimators: the unconditional cumulative distribution estimator and the conditional cumulative distribution estimator were examined. Simulation study was conducted, the mean square error of the unconditional cumulative distribution estimator was found to be smaller in comparison to its conditional cumulative distribution estimator counterpart. Hence, we recommend the use of the former.