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Hypothesis testing for mean vector and covariance matrix of multi-populations under a two-step monotone incomplete sample in large sample and dimension

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  • Tsukada, Shin-ichi

Abstract

In this study, we focus on the critical issue of analyzing data sets with missing data. Statistically processing such data sets, particularly those with general missing data, is challenging to express in explicit formulae, and often requires computational algorithms to solve. We specifically address monotone missing data, which are the simplest form of data sets with missing data. We conduct hypothesis tests to determine the equivalence of mean vectors and covariance matrices across different populations. Furthermore, we derive the properties of likelihood ratio test statistics in scenarios involving large samples and large dimensions.

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  • 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).
    • Handle: RePEc:eee:jmvana:v:202:y:2024:i:c:s0047259x23001367
    DOI: 10.1016/j.jmva.2023.105290
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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. Yu, Jianqi & Krishnamoorthy, K. & Pannala, Maruthy K., 2006. "Two-sample inference for normal mean vectors based on monotone missing data," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2162-2176, November.
    4. 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.
    5. 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.
    6. 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.
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