Testing for Normality with Neural Networks

TL;DR

This paper introduces a neural network-based method for testing normality that outperforms traditional tests in accuracy and power, especially on small samples, with near-perfect AUROC scores.

Contribution

The paper presents a novel neural network approach for normality testing that surpasses standard tests in accuracy and applicability to small samples.

Findings

Neural network achieved AUROC close to 1 on small samples.

Network accuracy exceeded 96% on larger samples.

Outperformed traditional normality tests like Shapiro-Wilk and Anderson-Darling.

Abstract

In this paper, we treat the problem of testing for normality as a binary classification problem and construct a feedforward neural network that can successfully detect normal distributions by inspecting small samples from them. The numerical experiments conducted on small samples with no more than 100 elements indicated that the neural network which we trained was more accurate and far more powerful than the most frequently used and most powerful standard tests of normality: Shapiro-Wilk, Anderson-Darling, Lilliefors and Jarque-Berra, as well as the kernel tests of goodness-of-fit. The neural network had the AUROC score of almost 1, which corresponds to the perfect binary classifier. Additionally, the network's accuracy was higher than 96% on a set of larger samples with 250-1000 elements. Since the normality of data is an assumption of numerous techniques for analysis and inference, the neural network constructed in this study has a very high potential for use in everyday practice of statistics, data analysis and machine learning in both science and industry.