On noncentral Wishart mixtures of noncentral Wisharts and their use for testing random effects in factorial design models
arXiv:2502.13711 · doi:10.1016/j.jmaa.2025.129897
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 -dimensional normal data, thereby broadening the findings of Bilodeau [ArXiv (2022), 6 pp.], who treated the case . The same approach makes it possible to test random effects in more general factorial design models.
12 pages, 0 figures, 2 tables