插补还是不插补？在不完整数据集上检验多元正态性：重新审视 BHEP 检验
To impute or not to? Testing multivariate normality on incomplete dataset: Revisiting the BHEP test
AI总结：
针对完全随机缺失数据下的多元正态性 BHEP 检验，本文比较完整案例分析与插补方法的渐近性质和功效，并提出 bootstrap 算法以恢复插补情形下的 p 值近似。
摘要：
本文聚焦于在数据完全随机缺失的情况下，使用 BHEP 检验进行多元正态性检验。我们的目标有两个：首先，深入理解在两种广泛使用的缺失数据处理方法（即完整案例分析和插补）下，BHEP 检验统计量的渐近行为；其次，比较这些方法下检验统计量的功效表现。研究观察到，在插补方法下，检验统计量的仿射不变性未能得到保持。为解决这一问题，我们提出了一种适当的 bootstrap 算法来近似 p 值。大量模拟研究表明，与采用完整案例分析的检验相比，均值法和中位数法均表现出更高的功效，并提出了若干有待进一步研究的问题。
英文摘要：
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.
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