Multiple kernel procedure: An asymptotic support

This paper deals with kernel non-parametric estimation. The multiple kernel method, as proposed by Berlinet (1993), consists in choosing both the smoo thing parameter and the order of the kernel function. In this paper we foll ow this general idea, and the selection is carried out by a combination of plug-in and cross-validation techniques. In a first attempt we give an asym ptotic optimality theorem which is stated in a general unifying setting tha t includes many curve estimation problems. Then, as an illustration, it wil l be seen how this behaves in both special cases of kernel density and kern el regression estimation.