| Title | Exact and near-exact distributions for the likelihood ratio test statistics used to test for stationarity and circularity in multivariate models |
| Publication Type | Unpublished |
| Year of Publication | 2011 |
| Authors | Coelho CA, Oliveira S, Marques FJ |
| Series Title | Preprint |
| Keywords | Circular covariance matrix, product of independent Beta random variables, sums of independent Gamma random variables, sums of independent Logbeta r.v.’s |
| Abstract | In this paper we obtain the exact distribution for the likelihood ratio test (l.r.t.) statistics to test that in a multivariate normal model: i) the mean vector is null and the covariance matrix is circular, ii) the means in the mean vector are all equal and the covariance matrix is circular. The authors show that in the first case the exact distribution of the negative logarithm of the l.r.t. statistic may be written as an infinite mixture of Generalized Near-Integer Gamma (GNIG) distributions, while in the second case it is a Generalized Integer Gamma (GIG) distribution. For the first l.r.t. statistic, in which case the exact distribution is less manageable, it is thus desirable and useful the development of near-exact distributions. Quite extensive numerical studies and simulations show the very high closeness of these near-exact distributions to the exact distribution as well as their very good asymptotic properties. |
| URL | http://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2011/5_11.pdf |
