A neural network approach to normality testing

Abstract

The aim of this work is to provide a new approach to the classical problem of determining whether or not a set of data has been sampled from a univariate normal distribution. A simple neural network architecture is proposed as an efficient way of combining and reinforcing the discriminatory capabilities of different popular statistics commonly used in conventional hypothesis testing procedures. Special emphasis is placed on the fact that these procedures lack a reliable measure of the degree to which the observed data supports the normality assumption. Several authors have shown that the so-called P-values are inefficient and ambiguous when dealing with this matter, so the Bayesian posterior probabilities are suggested as the best candidates to play this role. For this reason, a significant part of our work has focused on training the neural networks so that their outputs accurately approximate these probabilities.