Multivariate normality test based on Shannon's entropy

Checking normality before applying statistical methods is essential for ensuring that statistical inferences are accurate. This paper focuses on the multivariate normality test. The proposed test statistics are inspired by the univariate entropy test. The univariate entropy statistics for each dimension are aggregated to obtain an overall test statistic. To address issues related to singular sample covariance matrices in high-dimensional cases, a sparse precision matrix estimation method is employed. Monte Carlo simulations are conducted to compare the performance of the proposed method with some existing statistics. The application of the proposed method to human body-fat data and colon cancer data highlights the importance of normality testing in statistical analysis.