Testing multivariate normality by testing independence
This provides a potentially more efficient method for statisticians and data analysts to test multivariate normality, especially in high-dimensional settings, though it appears incremental as it builds on existing independence tests.
The authors tackled the problem of testing multivariate normality by proposing a test based on Kac-Bernstein's characterization, which uses existing independence tests for sums and differences of data samples, and found that it may be more efficient for high-dimensional data compared to alternative methods.
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}.