To impute or not to? Testing multivariate normality on incomplete dataset: Revisiting the BHEP test

In this paper, we focus on testing multivariate normality using the BHEP test with data that are missing completely at random. Our objective is twofold: first, to gain insight into the asymptotic behavior of BHEP test statistics under two widely used approaches for handling missing data, namely complete-case analysis and imputation, and second, to compare the power performance of test statistic under these approaches. It is observed that under the imputation approach, the affine invariance of test statistics is not preserved. To address this issue, we propose an appropriate bootstrap algorithm for approximating p-values. Extensive simulation studies demonstrate that both mean and median approaches exhibit greater power compared to testing with complete-case analysis, and open some questions for further research.