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| Título | Near-exact distributions for the likelihood ratio test statistic of the multi-sample block-matrix sphericity test |
| Publication Type | Unpublished |
| Year of Publication | 2009 |
| Authors | Marques FJ, Coelho CA |
| Series Title | Preprint |
| Palavras-chave | asymptotic distributions, mixtures, multi-sample block-matrix sphericity test, near-exact distributions |
| Abstract | The multi-sample block-matrix sphericity test and its particular cases have wide applications in testing the error strucutre in several multivariate linear models. However, the practical implementation of this test has been hindered by difficulties in handling the exact distribution of the associated statistic and the non-availability in the literature of well-fit asymptotic distributions. We use a decomposition of the null hypothesis into conditionally independent hypotheses in order to induce a factorization of the likelihood ratio test (l.r.t.) statistic. We then use the induced factorization of the characteristic function of the logarithm of the l.r.t. statistic to obtain very well-fit but highly manageable near-exact distributions for the l.r.t. statistic of this test and its particular cases. These near-exact distributions will allow for the easy computation of well-fit near-exact quantiles and p-values, enabling this way a more frequent practical use of these tests. A measure of proximity between distributions, based on the corresponding characteristic functions, is used to assess the performance of the near-exact distributions. |
| URL | http://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2009/1_09.pdf |