Testing multivariate normality by testing independence

Abstract

We propose a simple multivariate normality test based on Kac-Bernstein's characterization, which can be conducted by utilising existing statistical independence tests for sums and differences of data samples. We also perform its empirical investigation, which reveals that for high-dimensional data, the proposed approach may be more efficient than the alternative ones. The accompanying code repository is provided at \url{https://shorturl.at/rtuy5}.