| Title | A general approach to the exact and near-exact distributions of the main likelihood ratio test statistics used in the complex multivariate Normal setting |
| Publication Type | Unpublished |
| Year of Publication | 2011 |
| Authors | Coelho CA, Marques FJ, Arnold BC |
| Series Title | Preprint |
| Keywords | equality of covariance matrices, equality of mean vectors, Generalized Integer Gamma distribution, Generalized Near-Integer Gamma distribution, independence, mixtures, nullity of expected mean matrix, sphericity |
| Abstract | In this paper the authors show how, in parallel with what happens in the real case, it is possible to establish a common structure for the exact distribution of the main likelihood ratio test (l.r.t.) statistics used in the complex multivariate Normal setting. This leads to simple expressions for the exact distribution of some of these statistics and to very well-performing approximations for the distribution of the other statistics. Easy to implement near-exact distributions are developed for the l.r.t. statistics to test sphericity and the equality of covariance matrices. Numerical studies show how these near-exact distributions outperform by far any other available approximations. |
| URL | http://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2011/19_11.pdf |
