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| Título | Another look at the exact and near-exact distributions for the most common likelihood ratio test statistics used in multivariate analysis |
| Publication Type | Unpublished |
| Year of Publication | 2010 |
| Authors | Coelho CA, Arnold BC, Marques FJ |
| Series Title | Preprint |
| Palavras-chave | equality of mean vectors test, Generalized Near-Integer Gamma distribution, independence test, mixtures of Gamma distributions, sphericity test, test of equality of covariance matrices |
| Abstract | In this paper we will show how, using an expansion of a Logbeta distribution as an infinite mixture of Gamma distributions we are able to obtain near-exact distributions for the negative logarithm of the likelihood ratio test statistics used in Multivariate Analysis to test the independence of several sets of variables, the equality of several mean vectors, sphericity and the equality of several variance-covariance matrices as finite mixtures of Generalized Near-Integer Gamma distributions. These near-exact distributions will match as many of the exact moments as we wish and we will be able to have an a priori upper-bound for the difference between their c.d.f. and the exact c.d.f.. These near-exact distributions also display very good performance, with an agreement with the exact distribution which may virtually be taken as far as we wish and which it is not possible to obtain with the usual asymptotic distributions. |
| URL | http://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2010/14_10.pdf |