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, 3403-3415 p.Article in journal (Refereed) Published
A characterization of the distribution of the multivariate quadratic form given by XAX', where X is a p x n normally distributed matrix and A is an n x 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 non central Wishart 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
2012. Vol. 41, no 18, 3403-3415 p.
Eigenvalues, Non central Wishart distribution, Quadratic form, Singular matrix normal distribution, Spectral decomposition
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:kth:diva-88909DOI: 10.1080/03610926.2011.563009ISI: 000308465400007ScopusID: 2-s2.0-84866102564OAI: oai:DiVA.org:kth-88909DiVA: diva2:502600
QC 201210042012-02-142012-02-142015-03-04Bibliographically approved