Feedforward networks have demonstrated their ability to model non-linear data. Despite this success, their use as a statistical analysis tool has been limited by the persistent assumption that these networks can only be implemented as non-parametric models. In fact, a feedforward network can be used for parametric modeling, with the result that many of the common parametric testing procedures can be applied to the non-linear network. In this paper, a feedforward network for predicting the biological growth rate of pickles is developed. Using this network, the parametric nature of the network is demonstrated. Once trained, the network model is tested using standard parametric methods. In order to facilitate this testing, it is first necessary to develop a method for calculating the degrees of freedom for the neural network, and the residual covariance matrix. It is shown that the degrees of freedom is determined by the number of parameters that actually contribute to an output. With this information, the covariance matrix can be created by adapting the error matrix. Using these results, the trained network is tested using a simple F-statistic.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty