Estimating data dispersion using neural networks

Neural networks have often been used to approximate the conditional mean of a random variable (RV). In this paper a scheme for parametric statistical estimation developed by H. White is applied to estimation of the conditional variance of an RV using a neural network. By requiring a network to approximate a conditional probability density function, the variance estimates are learned without explicit targets. As shown by White, the method results in an information-theoretically optimal estimate of the dispersion of the RV under reasonable assumptions. The method is implemented and applied to a simple problem with promising results