| Título | Testing of hypothesis of a block compound symmetric covariance matrix |
| Publication Type | Unpublished |
| Year of Publication | 2013 |
| Authors | Coelho CA, Roy A |
| Series Title | Preprint |
| Palavras-chave | characteristic function, composition of hypothesis, distribution of likelihood ratio statistics, near-exact distributions, product of independent Beta random variables, sum of independent Gamma random variables. |
| Abstract | In this paper the authors study the problem of testing the hypothesis of a block compound symmetry covariance matrix with two-level multivariate observations, taken for m variables over u sites or time points. Through the decomposition of the main hypothesis into two sub-hypotheses, the likelihood ratio test statistic is easily obtained as well as its exact moments. Its exact distribution is then analyzed. Because this distribution is quite elaborate, yielding a non-manageable distribution function, a manageable but very precise near-exact distribution is developed. Numerical studies conducted to evaluate the closeness between this near-exact distribution and the exact distribution show the very good performance of this approximation even for very small sample sizes. A real data example is studied and a simulation is also conducted. |
| URL | http://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2013/1_13.pdf |
