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On the exact and approximate distributions of the product of a Wishart matrix with a normal vector

Bodnar, Taras ; Mazur, Stepan LU and Okhrin, Yarema (2013) In Journal of Multivariate Analysis 122. p.70-81
Abstract
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... (More)
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. (Less)
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author
; and
publishing date
type
Contribution to specialist publication or newspaper
publication status
published
subject
keywords
Wishart distribution, Multivariate normal distribution, Stochastic representation, Integral approximation
categories
Popular Science
in
Journal of Multivariate Analysis
volume
122
pages
70 - 81
publisher
Academic Press
external identifiers
  • scopus:84882656396
ISSN
0047-259X
DOI
10.1016/j.jmva.2013.07.007
language
English
LU publication?
no
id
3f490b6a-6b91-4f79-99b0-df10c4c5de32 (old id 8082821)
date added to LUP
2016-04-01 13:20:19
date last changed
2020-03-24 03:08:00
@misc{3f490b6a-6b91-4f79-99b0-df10c4c5de32,
  abstract     = {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.},
  author       = {Bodnar, Taras and Mazur, Stepan and Okhrin, Yarema},
  issn         = {0047-259X},
  language     = {eng},
  pages        = {70--81},
  publisher    = {Academic Press},
  series       = {Journal of Multivariate Analysis},
  title        = {On the exact and approximate distributions of the product of a Wishart matrix with a normal vector},
  url          = {http://dx.doi.org/10.1016/j.jmva.2013.07.007},
  doi          = {10.1016/j.jmva.2013.07.007},
  volume       = {122},
  year         = {2013},
}