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Testing multivariate normality in incomplete data of small sample size

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  • Tan, Ming
  • Fang, Hong-Bin
  • Tian, Guo-Liang
  • Wei, Gang

Abstract

In longitudinal studies with small samples and incomplete data, multivariate normal-based models continue to be a powerful tool for analysis. This has included a broad scope of biomedical studies. Testing the assumption of multivariate normality (MVN) is critical. Although many methods are available for testing normality in complete data with large samples, a few deal with the testing in small samples. For example, Liang et al. (J. Statist. Planning and Inference 86 (2000) 129) propose a projection procedure for testing MVN for complete-data with small samples where the sample sizes may be close to the dimension. To our knowledge, no statistical methods for testing MVN in incomplete data with small samples are yet available. This article develops a test procedure in such a setting using multiple imputations and the projection test. To utilize the incomplete data structure in multiple imputation, we adopt a noniterative inverse Bayes formulae (IBF) sampling procedure instead of the iterative Gibbs sampling to generate iid samples. Simulations are performed for both complete and incomplete data when the sample size is less than the dimension. The method is illustrated with a real study on an anticancer drug.

Suggested Citation

  • Tan, Ming & Fang, Hong-Bin & Tian, Guo-Liang & Wei, Gang, 2005. "Testing multivariate normality in incomplete data of small sample size," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 164-179, March.
    • Handle: RePEc:eee:jmvana:v:93:y:2005:i:1:p:164-179
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    References listed on IDEAS

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    1. Henze, Norbert & Wagner, Thorsten, 1997. "A New Approach to the BHEP Tests for Multivariate Normality," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 1-23, July.
    2. Romeu, J. L. & Ozturk, A., 1993. "A Comparative Study of Goodness-of-Fit Tests for Multivariate Normality," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 309-334, August.
    3. Ming Tan & Hong-Bin Fang & Guo-Liang Tian & Peter J. Houghton, 2002. "Small-Sample Inference for Incomplete Longitudinal Data with Truncation and Censoring in Tumor Xenograft Models," Biometrics, The International Biometric Society, vol. 58(3), pages 612-620, September.
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    1. Najarzadeh, Dariush, 2020. "A simple test for zero multiple correlation coefficient in high-dimensional normal data using random projection," Computational Statistics & Data Analysis, Elsevier, vol. 148(C).
    2. Liang, Jiajuan & Tang, Man-Lai, 2009. "Generalized F-tests for the multivariate normal mean," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1177-1190, February.
    3. Bruno Ebner & Norbert Henze, 2020. "Tests for multivariate normality—a critical review with emphasis on weighted $$L^2$$ L 2 -statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 845-892, December.
    4. Daniel McNeish, 2017. "Missing data methods for arbitrary missingness with small samples," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(1), pages 24-39, January.
    5. Liang, Jiajuan & Tang, Man-Lai & Chan, Ping Shing, 2009. "A generalized Shapiro-Wilk W statistic for testing high-dimensional normality," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3883-3891, September.

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