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Sphericity test in a GMANOVA-MANOVA model with normal error

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  • Bai, Peng

Abstract

For the GMANOVA-MANOVA model with normal error: , , we study in this paper the sphericity hypothesis test problem with respect to covariance matrix: [Sigma]=[lambda]Iq ([lambda] is unknown). It is shown that, as a function of the likelihood ratio statistic [Lambda], the null distribution of [Lambda]2/n can be expressed by Meijer's function, and the asymptotic null distribution of -2log[Lambda] is (as n-->[infinity]). In addition, the Bartlett type correction -2[rho]log[Lambda] for log[Lambda] is indicated to be asymptotically distributed as with order n-2 for an appropriate Bartlett adjustment factor -2[rho] under null hypothesis.

Suggested Citation

  • Bai, Peng, 2009. "Sphericity test in a GMANOVA-MANOVA model with normal error," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2305-2312, November.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:10:p:2305-2312
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    Cited by:

    1. Guanghui Min & Muhui Lin & Ying Liu & Ning Yang & Zhe Li, 2023. "Research on the Evaluation Model of School Management Quality in the Compulsory Education Stage Based on Big Data Technology," Sustainability, MDPI, vol. 15(13), pages 1-15, June.
    2. Vargas, Tiago M. & Ferrari, Silvia L.P. & Lemonte, Artur J., 2014. "Improved likelihood inference in generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 110-124.
    3. Marton Gosztonyi, 2023. "Comparative Analysis of X-Y-Z Generation Entrepreneurs in a Semi-Peripheral EU Member Country: Insights from Regularized Regression Techniques," European Research Studies Journal, European Research Studies Journal, vol. 0(4), pages 191-217.

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