An approximation result for nets in functional estimation

In this paper a quantitative approximation result is obtained for a general class of function nets which is of interest in functional estimation. Specific applications are given to approximation by neural nets, radial basis function nets, and wavelet nets. For the proof we combine the empirical process based results of a paper of Yukich et al. (IEEE Trans. Inform. Theory 41 (4) (1995) 1021) with probabilistic based approximation results of Makovoz (J. Approx. Theory 85 (1996) 98) for the optimal approximation of functions by convex combination of n basis elements.