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.

翻译：本文聚焦于在完全随机缺失数据条件下，使用BHEP检验进行多元正态性检验。研究目标有二：其一，深入理解在两种常用缺失数据处理方法（完整案例分析法和插补法）下BHEP检验统计量的渐近行为；其二，比较这两种方法下检验统计量的功效表现。研究发现，采用插补法时，检验统计量的仿射不变性未能保持。为解决此问题，我们提出了一种适用于近似p值的自举算法。大量模拟研究表明，与完整案例分析法相比，均值插补法和中位数插补法均展现出更高的检验功效，并为后续研究提出了若干待解问题。