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Distribution of the product of a singular Wishart matrix and a normal vector
Department of Mathematics, Humboldt-University of Berlin, Berlin, Germany .
Department of Statistics, Lund University, Lund, Sweden. (Statistics)
Department of Statistics, University of Augsburg, Augsburg, Germany.
2014 (English)In: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, no 91, 1-15 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we derive a very useful formula for the stochastic representation of the product of a singular Wishart matrix with a normal vector. Using this result, the expressions of the density function as well as of the characteristic function are established. Moreover, the derived stochastic representation is used to generate random samples from the product which leads to a considerable improvement in the computation efficiency. Finally, we present several important properties of the singular Wishart distribution, like its characteristic function and distributional properties of the partitioned singular Wishart matrix. 

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2014. no 91, 1-15 p.
Keyword [en]
Singular Wishart distribution, multivariate normal distribution, stochastic representation, characteristic function.
National Category
Probability Theory and Statistics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-54841DOI: 10.1090/tpms/962Scopus ID: 2-s2.0-84945119905OAI: oai:DiVA.org:oru-54841DiVA: diva2:1066858
Available from: 2017-01-19 Created: 2017-01-19 Last updated: 2017-10-18Bibliographically approved

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