Consistency of error density and distribution function estimators in nonparametric regression

Abstract

This paper considers the problem of estimating the error density and distribution function in nonparametric regression models. Sufficient conditions are given under which the histogram error density estimator based on nonparametric residuals is uniformly weakly and strongly consistent, and L1-consistent. The uniform consistency with a rate of the nonparametric residual empirical distribution function and the histogram error density estimator is also established.Histogram density estimation Nonparametric residuals Empirical process