Asymptotic distributions of error density and distribution function estimators in nonparametric regression

This paper considers the problem of estimating the error density and distribution functions in nonparametric regression models. The asymptotic distribution of a suitably standardized density estimator at a fixed point is shown to be normal while that of the maximum of a suitably normalized deviation of the density estimator from the true density function is the same as in the case of the one sample set up. Finally, the standardized residual empirical process is shown to be uniformly close to the similarly standardized empirical process of the errors. This paper thus generalizes some of the well known results about the residual density estimators and the empirical process in parametric regression models to nonparametric regression models, thereby enhancing the domain of their applications.