The Neural Network Analysis of Normality of Small Samples of Biometric Data through Using the Chi-Square Test and Anderson–Darling Criteria
Vladimir I. Volchikhin
Aleksandr I. Ivanov
Alexander V. Bezyaev
Evgeniy N. Kupriyanov
Introduction. The aim of the work is to reduce the requirements to test sample size when testing the hypothesis of normality.
Materials and Methods. A neural network generalization of three well-known statistical criteria is used: the chi-square criterion, the Anderson–Darling criterion in ordinary form, and the Anderson–Darling criterion in logarithmic form.
Results. The neural network combining of the chi-square criterion and the Anderson–Darling criterion reduces the sample size requirements by about 40 %. Adding a third neuron that reproduces the logarithmic version of the Andersоn–Darling test leads to a small decrease in the probability of errors by 2 %. The article deals with single-layer and multilayer neural networks, summarizing many currently known statistical criteria.
Discussion and Conclusion. An assumption has been made that an artificial neuron can be assigned to each of the known statistical criteria. It is necessary to change the attitude to the synthesis of new statistical criteria that previously prevailed in the 20th century. There is no current need for striving to create statistical criteria for high power. It is much more advantageous trying to ensure that the data of newly synthesized statistical criteria are low correlated with many of the criteria already created.
Keywords: chi-square test, Anderson–Darling criterion, artificial neural network, statistical criterion, neural network reproduction of statistical criteria, neural network analysis, small sample
For citation: Volchikhin V.I., Ivanov A.I., Bezyaev A.V., Kupriyanov E.N. The Neural Network Analysis of Normality of Small Samples of Biometric Data through Using the Chi-Square Test and Anderson–Darling Criteria. Inzhenernyye tekhnologii i sistemy = Engineering Technologies and Systems. 2019; 29(2):205-217. DOI: https://doi.org/10.15507/2658-4123.029.201902.205-217
Contribution of the authors: V. I. Volchikhin – the development of the concept of a neural network association of statistical criteria; A. I. Ivanov – the formalization of the neural network description of the statistical criteria under consideration; A. V. Bezyaev – the adjustment of the output codes of a neural network that generalizes statistical criteria; E. N. Kupriyanov – the software implementation of calculations and formation of tables with data.
All authors have read and approved the final version of the paper.
Received 15.02.2019; revised 25.04.2019; published online 28.06.2019
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