Equivalent number of degrees of freedoms for neural networks.

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