%0 Journal Article
%T Rate-optimal estimation for a general class of nonparametric regression models with unknown link functions
%A Joel L. Horowitz
%A Enno Mammen
%J Mathematics
%D 2008
%I arXiv
%R 10.1214/009053607000000415
%X This paper discusses a nonparametric regression model that naturally generalizes neural network models. The model is based on a finite number of one-dimensional transformations and can be estimated with a one-dimensional rate of convergence. The model contains the generalized additive model with unknown link function as a special case. For this case, it is shown that the additive components and link function can be estimated with the optimal rate by a smoothing spline that is the solution of a penalized least squares criterion.
%U http://arxiv.org/abs/0803.2999v1