On noncentral Wishart mixtures of noncentral Wisharts and their use for testing random effects in factorial design models
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912952612814848 |
|---|---|
| author | Genest, Christian MacKay, Anne Ouimet, Frédéric |
| author_facet | Genest, Christian MacKay, Anne Ouimet, Frédéric |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13711 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On noncentral Wishart mixtures of noncentral Wisharts and their use for testing random effects in factorial design models Genest, Christian MacKay, Anne Ouimet, Frédéric Statistics Theory Probability Applications 60E05, 60E10, 62E15, 62F03, 62H10, 62H15, 62H25, 62K10, 62K15 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. |
| title | On noncentral Wishart mixtures of noncentral Wisharts and their use for testing random effects in factorial design models |
| topic | Statistics Theory Probability Applications 60E05, 60E10, 62E15, 62F03, 62H10, 62H15, 62H25, 62K10, 62K15 |
| url | https://arxiv.org/abs/2502.13711 |