Exact nonnull distribution of Wilks' statistic : the ratio and product of independent components

dc.contributor.authorBekker, Andriette, 1958-
dc.contributor.authorRoux, Jacobus J.J.
dc.contributor.authorArashi, Mohammad
dc.contributor.emailandriette.bekker@up.ac.zaen_US
dc.date.accessioned2011-02-22T09:39:29Z
dc.date.available2011-02-22T09:39:29Z
dc.date.issued2011-03
dc.description.abstractThe study of the noncentral matrix variate beta type distributions has been sidelined because the final expressions for the densities depend on an integral that has not been resolved in an explicit way. We derive an exact expression for the nonnull distribution of Wilks’ statistic and precise expressions for the densities of the ratio and product of two independent components of matrix variates where one matrix variate has the noncentral matrix variate beta type I distribution and the other has the matrix variate beta type I distribution. We provide the expressions for the densities of the determinant of the ratio and the product of these two components. These distributions play a fundamental role in various areas of statistics, for example in the criteria proposed by Wilks.en
dc.identifier.citationBekker, A, Roux, JJJ & Arashi, M 2011, 'Exact nonnull distribution of Wilks' statistic : the ratio and product of independent components', Journal of Multivariate Analysis, vol. 102, no. 3, pp. 619-628. [http://www.elsevier.com/locate/jmva]en
dc.identifier.issn0047-259X
dc.identifier.other10.1016/j.jmva.2010.11.005
dc.identifier.urihttp://hdl.handle.net/2263/15917
dc.language.isoenen_US
dc.publisherElsevieren_US
dc.rights© 2010 Elsevier Inc.en_US
dc.subjectInvariant polynomialsen
dc.subjectMeijer’s G-functionen
dc.subjectNoncentral matrix variate beta type Ien
dc.subjectNonnull distributionen
dc.subjectWilks’ statisticen
dc.subject.lcshZonal polynomialsen
dc.subject.lcshMatricesen
dc.titleExact nonnull distribution of Wilks' statistic : the ratio and product of independent componentsen
dc.typePostprint Articleen

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