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On the exact and approximate distributions of the product of a Wishart matrix with a normal vector
Department of Mathematics, Humboldt University of Berlin, Berlin, Germany.
Department of Statistics, European University Viadrina, Frankfurt(Oder), Germany. (Statistics)
Department of Statistics, University of Augsburg, Augsburg, Germany.
2013 (English)In: Journal of Multivariate Analysis, ISSN 0047-259X, E-ISSN 1095-7243, Vol. 122, 70-81 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we consider the distribution of the product of a Wishart random matrix and a Gaussian random vector. We derive a stochastic representation for the elements of the product. Using this result, the exact joint density for an arbitrary linear combination of the elements of the product is obtained. Furthermore, the derived stochastic representation allows us to simulate samples of arbitrary size by generating independently distributed chi-squared random variables and standard multivariate normal random vectors for each element of the sample. Additionally to the Monte Carlo approach, we suggest another approximation of the density function, which is based on the Gaussian integral and the third order Taylor expansion. We investigate, with a numerical study, the properties of the suggested approximations. A good performance is documented for both methods. 

Place, publisher, year, edition, pages
Elsevier, 2013. Vol. 122, 70-81 p.
Keyword [en]
Wishart distribution, Multivariate normal distribution, Stochastic representation, Integral approximation
National Category
Probability Theory and Statistics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-54840DOI: 10.1016/j.jmva.2013.07.007ISI: 000325303400005Scopus ID: 2-s2.0-84882656396OAI: oai:DiVA.org:oru-54840DiVA: diva2:1066855
Note

Funding Agency:

German Science Foundation (DFG) BO3521/2  OK103/1

Available from: 2017-01-19 Created: 2017-01-19 Last updated: 2017-10-18Bibliographically approved

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Citation style
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