On a projection estimator of the regression function derivative

In this paper, we study the estimation of derivative a regression function in standard univariate model. The estimators are defined either by derivating nonparametric least-squares or estimating projection derivative. We prove two simple risk bounds allowing to compare our estimators. More elaborate under stability assumption then provided. Bases and spaces on which can illustrate assumptions first results both compact non type, discuss rates reached They turn out be optimal case. Lastly, propose model selection procedure associated bound. To consider bases with support makes problem difficult.