Equivalent number of degrees of freedom for neural networks

The notion of equivalent number of degrees of freedom (e.d.f.) to be used in neural network modeling from small datasets has been introduced in Ingrassia and Morlini (2005). It is much smaller than the total number of parameters and it does not depend on the number of input variables. We generalize our previous results and discuss the use of the e.d.f. in the general framework of multivariate nonparametric model selection. Through numerical simulations, we also investigate the behavior of model selection criteria like AIC, GCV and BIC/SBC, when the e.d.f. is used instead of the total number of the adaptive parameters in the model.