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Theory of Probability and Mathematical Statistics

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On the asymptotic and approximate distributions of the product of an inverse Wishart matrix and a Gaussian vector


Authors: I. Kotsiuba and S. Mazur
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 93 (2015).
Journal: Theor. Probability and Math. Statist. 93 (2016), 103-112
MSC (2010): Primary 62E17, 62E20
DOI: https://doi.org/10.1090/tpms/1004
Published electronically: February 7, 2017
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Abstract: In this paper we study the distribution of the product of an inverse Wishart random matrix and a Gaussian random vector. We derive its asymptotic distribution as well as a formula for its approximate density function which is based on the Gaussian integral and the third order Taylor expansion. Furthermore, we compare the asymptotic and approximate density functions with the exact density obtained by Bodnar and Okhrin (2011). The results obtained in the paper are confirmed by the numerical study.


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Additional Information

I. Kotsiuba
Affiliation: Department of Theoretical and Applied Statistics, Ivan Franko National University of Lviv, Universytetska 1, 79000, Lviv, Ukraine
Email: kotsiuba@hotmail.com

S. Mazur
Affiliation: Department of Statistics, Lund University, PO Box 743, SE-22007 Lund, Sweden
Email: stepan.mazur@stat.lu.se

DOI: https://doi.org/10.1090/tpms/1004
Keywords: Wishart distribution, multivariate normal distribution, asymptotic distribution, integral approximation
Received by editor(s): March 2, 2015
Published electronically: February 7, 2017
Additional Notes: The second author appreciates the financial support of the Swedish Research Council Grant Dnr: 2013-5180 and Riksbankens Jubileumsfond Grant Dnr: P13-1024:1
Article copyright: © Copyright 2017 American Mathematical Society

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