Rate-optimal estimation for a general class of nonparametric regression models with unknown link functions

摘要

This paper discusses a nonparametric regression model that naturallygeneralizes neural network models. The model is based on a finite number ofone-dimensional transformations and can be estimated with a one-dimensionalrate of convergence. The model contains the generalized additive model withunknown link function as a special case. For this case, it is shown that theadditive components and link function can be estimated with the optimal rate bya smoothing spline that is the solution of a penalized least squares criterion.