Residuals density estimation in nonparametric regression

For the fixed design regression model, a nonparametric estimate of the probability density function of the residuals is proposed and its basic properties are studied. This estimate should have direct impact on diagnostics of regression models of this type. The estimate proposed here is based on estimating the regression function at the regressor points thus giving estimates of the residuals. Then these residual estimators are used to construct a kernel estimate of residuals density. The estimate is shown, among other things, to be consistent and asymptotically normal.