Maximum Likelihood Neural Network Prediction Models

Neural networks have received much attention in recent years mostly by non‐statisticians. The purpose of this paper is to incorporate neural networks in a non‐linear regression model and obtain maximum likelihood estimates of the network parameters using a standard Newton‐Raphson algorithm. We use maximum likelihood estimators instead of the usual back‐propagation technique and compare the neural network predictions with predictions of quadratic regression models and with non‐parametric nearest neighbor predictions. These comparisons are made using data generated from a variety of functions. Because of the number of parameters involved, neural network models can easily over‐fit the data, hence validation of results is crucial.