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Multivariate normality test based on kurtosis with two-step monotone missing data

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  • Kurita, Eri
  • Seo, Takashi

Abstract

This paper deals with a sample measure of multivariate kurtosis, which is used as a test statistic in multivariate normality testing problems. We define a new multivariate sample kurtosis measure to provide a multivariate normality test for data with a two-step monotone missing structure. Furthermore, we derive its expectation and variance using a perturbation method. To evaluate the accuracy of a normal approximation, we conducted a Monte Carlo simulation for certain parameters. Finally, we present a numerical example to illustrate the proposed procedure.

Suggested Citation

  • Kurita, Eri & Seo, Takashi, 2022. "Multivariate normality test based on kurtosis with two-step monotone missing data," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:jmvana:v:188:y:2022:i:c:s0047259x21001020
    DOI: 10.1016/j.jmva.2021.104824
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    References listed on IDEAS

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    1. Sreenivasa Rao Jammalamadaka & Emanuele Taufer & Gyorgy H. Terdik, 2021. "On Multivariate Skewness and Kurtosis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 607-644, August.
    2. Kollo, Tõnu, 2008. "Multivariate skewness and kurtosis measures with an application in ICA," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2328-2338, November.
    3. Tsukada, Shin-ichi, 2014. "Equivalence testing of mean vector and covariance matrix for multi-populations under a two-step monotone incomplete sample," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 183-196.
    4. Hao, Jian & Krishnamoorthy, K., 2001. "Inferences on a Normal Covariance Matrix and Generalized Variance with Monotone Missing Data," Journal of Multivariate Analysis, Elsevier, vol. 78(1), pages 62-82, July.
    5. Tomoya Yamada & Megan Romer & Donald Richards, 2015. "Kurtosis tests for multivariate normality with monotone incomplete data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 532-557, September.
    6. Srivastava, M. S., 1984. "A measure of skewness and kurtosis and a graphical method for assessing multivariate normality," Statistics & Probability Letters, Elsevier, vol. 2(5), pages 263-267, October.
    7. Ming Zhou & Yongzhao Shao, 2014. "A powerful test for multivariate normality," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(2), pages 351-363, February.
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