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arXiv · 2502.13711

On noncentral Wishart mixtures of noncentral Wisharts and their use for testing random effects in factorial design models

Christian Genest·Anne MacKay·Frédéric Ouimet
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Abstract

It is shown that a noncentral Wishart mixture of noncentral Wishart distributions with the same degrees of freedom yields a noncentral Wishart distribution, thereby extending the main result of Jones and Marchand [Stat 10 (2021), Paper No. e398, 7 pp.] from the chi-square to the Wishart setting. To illustrate its use, this fact is then employed to derive the finite-sample distribution of test statistics for random effects in a two-factor factorial design model with $d$-dimensional normal data, thereby broadening the findings of Bilodeau [ArXiv (2022), 6 pp.], who treated the case $d = 1$. The same approach makes it possible to test random effects in more general factorial design models.

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Christian Genest, Anne MacKay, Frédéric Ouimet. 2025-02-19. On noncentral Wishart mixtures of noncentral Wisharts and their use for testing random effects in factorial design models. https://doi.org/10.1016/j.jmaa.2025.129897

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