Estimation of the density of regression errors by pointwise model selection

Abstract

To cite this version:Sandra Plancade. Estimation of the density of regression errors by pointwise model selection. Abstract. This paper presents two results: a density estimator and an estimator of regression error density. We first propose a density estimator constructed by model selection, which is adaptive for the quadratic risk at a given point. Then we apply this result to estimate the error density in an homoscedastic regression framework Yi = b(Xi) + ǫi, from which we observe a sample (Xi, Yi). Given an adaptive estimator b b of the regression function, we apply the density estimation procedure to the residualsWe get an estimator of the density of ǫi whose rate of convergence for the quadratic pointwise risk is the maximum of two rates: the minimax rate we would get if the errors were directly observed and the minimax rate of convergence of b b for the quadratic integrated risk.

Strong uniform consistency and asymptotic normality of a kernel based error density estimator in functional autoregressive models

“…He made developments under the customary assumption that the regression function is differentiable and the error density is twice differentiable. More recently, Plancade [20] proposed a density estimator constructed by model selection and applied it in the nonparametric regression framework.…”