Neural discriminant analysis

In this article the role of the bootstrap is highlighted for nonlinear discriminant analysis using a feedforward neural network model. Statistical techniques are formulated in terms of the principle of the likelihood of a neural-network model when the data consist of ungrouped binary responses and a set of predictor variables. We illustrate that the information criterion based on the bootstrap method is shown to be favorable when selecting the optimum number of hidden units for a neural-network model. In order to summarize the measure of goodness-of-fit, the deviance on fitting a neural-network model to binary response data can be bootstrapped. We also provide the bootstrap estimates of the biases of excess error in a prediction rule constructed by fitting to the training sample in the neural network model. We additionally propose bootstrap methods for the analysis of residuals in order to identify outliers and examine distributional assumptions in neural-network model fitting. These methods are illustrated through the analyzes of medical diagnostic data.