Non-parametric estimation of residual moments and covariance

The aim of non-parametric regression is to model the behaviour of a response vector Y in terms of an explanatory vector X, based only on a finite set of empirical observations. This is usually performed under the additive hypothesis Y=f(X)+R, where f(X)=(Y|X) is the true regression function and R is the true residual variable. Subject to a Lipschitz condition on f, we propose new estimators for the moments (scalar response) and covariance (vector response) of the residual distribution, derive their asymptotic properties and discuss their application in practical data analysis