Neural network integration of classical statistical tests for processing small samples of biometrics data

Abstract

The Aim of this paper is to increase the power of statistical tests through their joint application to reduce the requirement for the size of the test sample. Methods. It is proposed to combine classical statistical tests, i.e. chi square, Cram r-von Mises and Shapiro-Wilk by means of using equivalent artificial neurons. Each neuron compares the input statistics with a precomputed threshold and has two output states. That allows obtaining three bits of binary output code of a network of three artificial neurons. Results. It is shown that each of such criteria on small samples of biometric data produces high values of errors of the first and second kind in the process of normality hypothesis testing. Neural network integration of three tests under consideration enables a significant reduction of the probabilities of errors of the first and second kind. The paper sets forth the results of neural network integration of pairs, as well as triples of statistical tests under consideration. Conclusions. Expected probabilities of errors of the first and second kind are predicted for neural network integrations of 10 and 30 classical statistical tests for small samples that contain 21 tests. An important element of the prediction process is the symmetrization of the problem, when the probabilities of errors of the first and second kind are made identical and averaged out. Coefficient modules of pair correlation of output states are averaged out as well by means of artificial neuron adders. Only in this case the connection between the number of integrated tests and the expected probabilities of errors of the first and second kind becomes linear in logarithmic coordinates.