On the Distribution of Matrix Quadratic Forms
2012 (English)In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 41, no 18, 3403-315 p.Article in journal (Refereed) Published
A characterization of the distribution of the multivariate quadratic form given by XAX′, where X is a p×n normally distributed matrix and A is an n×n symmetric real matrix, is presented. We show that the distribution of the quadratic form is the same as the distribution of a weighted sum of noncentralWishart distributed matrices. This is applied to derive the distribution of the sample covariance between the rows of X when the expectation is the same for every column and is estimated with the regular mean.
Place, publisher, year, edition, pages
Taylor & Francis, 2012. Vol. 41, no 18, 3403-315 p.
Quadratic form; Spectral decomposition; Eigenvalues; Singular matrix normal distribution; Non-centralWishart distribution
IdentifiersURN: urn:nbn:se:liu:diva-18513DOI: 10.1080/03610926.2011.563009ISI: 000308465400007OAI: oai:DiVA.org:liu-18513DiVA: diva2:220119