Nonlinear models for neural networks.

Abstract

The most commonly used applications of hidden-layer feed forward neural networks are to fit curves to regression data or to provide a surface from which a classification rule can be found. From a statistical viewpoint, the principle underpinning these networks is that of nonparametric regression with sigmoidal curves being located and scaled so that their sum approximates the data well, and the underlying mechanism is that of nonlinear regression, with the weights of the network corresponding to parameters in the regression model, and the objective function implemented in the training of the network defining the error structure. The aim ofthe present study is to use these statistical insights to critically appraise the reliability and the precision of the predicted outputs from a trained hiddenlayer feed forward neural network.