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On the Distribution of Matrix Quadratic Forms
Linköpings universitet .
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics. (computational biostatistics)ORCID iD: 0000-0003-1489-8512
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
Abstract [en]

 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.
Keyword [en]
Eigenvalues, Non central Wishart distribution, Quadratic form, Singular matrix normal distribution, Spectral decomposition
National Category
Probability Theory and Statistics
URN: urn:nbn:se:kth:diva-88909DOI: 10.1080/03610926.2011.563009ISI: 000308465400007ScopusID: 2-s2.0-84866102564OAI: diva2:502600

QC 20121004

Available from: 2012-02-14 Created: 2012-02-14 Last updated: 2015-03-04Bibliographically approved

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Koski, Timo
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