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| Título | Near-exact distributions for the sphericity likelihood ratio test statistic |
| Publication Type | Unpublished |
| Year of Publication | 2006 |
| Authors | Marques FJ, Coelho CA |
| Series Title | Preprint |
| Abstract | In this paper three near-exact distributions are developed for the sphericity test statistic. The exact probability density function of this statistic is usually represented through the use of the Meijer G function, what renders the computation of quantiles impossible even for a moderately large number of variables. The main goal of this paper is thus twofold: to obtain near-exact distributions that i) lie closer to the exact distribution than the asymptotic distributions and also that ii) correspond to density and cumulative distribution functions practical to use, allowing for an easy way to determine quantiles. On the way, also two asymptotic distributions that lie closer to the exact distribution than the existing ones were developed. Three measures are considered to evaluate the proximity between the exact and the asymptotic distribution and near-exact distributions developed. As a reference we use the asymptotic distributionproposed by Box as well as some saddlepoint approximations developed by other authors. |
| URL | http://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2006/4_06.pdf |