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

Area of Science:

• Statistics
• Statistical inference
• Multivariate analysis

Background:

• Testing multivariate normality is crucial in statistical analysis.
• Missing data can significantly complicate statistical tests.
• Existing methods for handling missing data in normality tests have limitations.

Purpose of the Study:

• To investigate the behavior of the BHEP test statistics with missing data.
• To compare the power of the BHEP test under complete-case analysis and imputation.
• To propose a bootstrap algorithm for accurate p-value approximation.

Main Methods:

• The study analyzes the asymptotic behavior of BHEP test statistics.
• It compares complete-case analysis with imputation methods (mean and median).
• A novel bootstrap algorithm is developed for approximating p-values.

Main Results:

• Complete-case analysis can lead to substantial information loss.
• Testing on imputed data without adjustment can severely distort Type I error rates.
• The proposed bootstrap algorithm effectively approximates p-values.
• Imputation methods (mean and median) demonstrate superior power compared to complete-case analysis.

Conclusions:

• The bootstrap algorithm provides a robust solution for BHEP testing with missing data.
• Imputation strategies are more powerful than complete-case analysis for this test.
• Further research is warranted to explore optimal imputation techniques and their impact on multivariate normality testing.