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Distribution of Quadratic Forms
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.ORCID iD: 0000-0001-9896-4438
2007 (English)Conference paper (Other academic)
Abstract [en]

A well known fact is that when testing hypotheses for covariance matrices, distributions of quadratic forms arise. A generalization of the distribution of the multivariate quadratic form XAX', where X is a p times n normally distributed matrix and A is a n times n symmetric real matrix, is presented. It is shown that the distribution of the quadratic form is the same as the distribution of a weighted sum of noncentral Wishart distributed matrices.

Using this characterization of the distribution several properties of the quadratic form XAX' will be shown.

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URN: urn:nbn:se:liu:diva-67584OAI: diva2:411421
MatTriad 2007 - Bedlewo, Poland
Available from: 2011-04-18 Created: 2011-04-18 Last updated: 2014-09-29

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Ohlson, Martin
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Mathematical Statistics The Institute of Technology

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