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On the asymptotic and approximate distributions of the product of an inverse wishart matrix and a gaussian vector

Kotsiuba, Igor and Mazur, S. LU (2016) In Theory of Probability and Mathematical Statistics 93. p.103-112
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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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Asymptotic distribution, Integral approximation, Multivariate normal distribution, Wishart distribution
in
Theory of Probability and Mathematical Statistics
volume
93
pages
10 pages
publisher
American Mathematical Society (AMS)
external identifiers
  • scopus:85013681010
ISSN
0094-9000
DOI
10.1090/tpms/1004
language
English
LU publication?
yes
id
4369f146-7639-448b-a61c-2e570f9ac870
date added to LUP
2017-03-09 11:14:52
date last changed
2017-03-10 15:46:22
@article{4369f146-7639-448b-a61c-2e570f9ac870,
  abstract     = {<p>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.</p>},
  author       = {Kotsiuba, Igor and Mazur, S.},
  issn         = {0094-9000},
  keyword      = {Asymptotic distribution,Integral approximation,Multivariate normal distribution,Wishart distribution},
  language     = {eng},
  pages        = {103--112},
  publisher    = {American Mathematical Society (AMS)},
  series       = {Theory of Probability and Mathematical Statistics},
  title        = {On the asymptotic and approximate distributions of the product of an inverse wishart matrix and a gaussian vector},
  url          = {http://dx.doi.org/10.1090/tpms/1004},
  volume       = {93},
  year         = {2016},
}