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Equivalence testing of mean vector and covariance matrix for multi-populations under a two-step monotone incomplete sample

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  • Tsukada, Shin-ichi

Abstract

This paper investigates the hypothesis testing of a mean vector and covariance matrix for multi-populations in the context of two-step monotone incomplete data drawn from Np+q(μ,Σ), a multivariate normal population with mean μ and covariance matrix Σ. Three null hypotheses are considered, and the likelihood ratio criterion and Wald-type criterion are derived. On the basis of numerical simulations, the test that employs the Wald-type criterion is recommended.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:132:y:2014:i:c:p:183-196
    DOI: 10.1016/j.jmva.2014.08.005
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    References listed on IDEAS

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    1. Chang, Wan-Ying & Richards, Donald St. P., 2010. "Finite-sample inference with monotone incomplete multivariate normal data, II," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 603-620, March.
    2. Chang, Wan-Ying & Richards, Donald St.P., 2009. "Finite-sample inference with monotone incomplete multivariate normal data, I," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1883-1899, October.
    3. 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.
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    Cited by:

    1. Tsukada, Shin-ichi, 2024. "Hypothesis testing for mean vector and covariance matrix of multi-populations under a two-step monotone incomplete sample in large sample and dimension," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    2. Nobumichi Shutoh & Takahiro Nishiyama & Masashi Hyodo, 2017. "Bartlett correction to the likelihood ratio test for MCAR with two-step monotone sample," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 71(3), pages 184-199, August.
    3. 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).

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