On the Non Gaussian Asymptotics of the Likelihood Ratio Test Statistic for Homogeneity of Covariance
AbstractThe likelihood ratio test for m-sample homogeneity of covariance is notoriously sensitive to the violations of Gaussian assumptions. Its asymptotic behavior under non-Gaussian densities has been the subject of an abundant literature. In a recent paper, Yanagihara et al. (2005) show that the asymptotic distribution of the likelihood ratio test statistic, under arbitrary elliptical densities with finite fourth-order moments, is that of a linear combination of two mutually independent chi-square variables. Their proof is based on characteristic function methods, and only allows for convergence in distribution conclusions. Moreover, they require homokurticity among the m populations. Exploiting the findings of Hallin and Paindaveine (2008a), we reinforce that convergence-in-distribution result into a convergence-in- probability one —-that is, we explicitly decompose the likelihood ratio test statistic into a linear combination of two variables which are asymptotically independent chi-square —-and moreover extend it to the heterokurtic case.
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Bibliographic InfoPaper provided by ULB -- Universite Libre de Bruxelles in its series Working Papers ECARES with number 2008_039.
Length: 9 p.
Date of creation: 2008
Date of revision:
Publication status: Published by:
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-12-07 (All new papers)
- NEP-ECM-2008-12-07 (Econometrics)
- NEP-ORE-2008-12-07 (Operations Research)
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