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| Título | Near-exact distributions for the likelihood ratio test statistic for testing equality of several variance-covariance matrices (revisited) |
| Publication Type | Unpublished |
| Year of Publication | 2009 |
| Authors | Coelho CA, Marques FJ |
| Series Title | Preprint |
| Abstract | The exact distribution of the l.r.t. (likelihood ratio test) statistic to test the equality of several variance-covariance matrices, as it also happens with several other l.r.t. statistics used in Multivariate Statistics, has a non-manageable form. This renders the computation of exact p-values and quantiles almost impossible, even for small numbers of variables. On the other hand, the existing asymptotic approximations do not exhibit the necessary precision for small sample sizes and their precision for larger samples is believed to be possible to be improved by using a different approach. For these reasons, the development of near-exact approximations to the distribution of this statistic, arising from an whole different method of approximating distributions, emerges as a desirable goal. From a factorization of the exact c.f. of the statistic where we adequately replace some of the factors, we obtain a near-exact c.f. which determines the near-exact distribution. This distribution, while being manageable lies much closer to the exact distribution than the available asymptotic distributions and opposite to these, is also asymptotic for increasing number of variables and matrices involved in the test. The evaluation of the performance of the distributions developed is done through the use of two measures based on the c.f.'s. Modules programmed in Mathematica are provided to compute p-values as well as the p.d.f., c.d.f. and c.f. of the near-exact distributions proposed. |
| URL | http://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2009/9_09.pdf |