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

Bodnar, Taras; Mazur, Stepan; Okhrin, Yarema

doi:10.1016/j.jmva.2013.07.007

Cited by 16 publications

(14 citation statements)

References 9 publications

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“…In this section, we present the main results of the paper which are complementary to the ones obtained in Bodnar et al [3,4] to the case of high-dimensional data and singular covariance matrix.…”

Section: Resultsmentioning

confidence: 57%

On the product of a singular Wishart matrix and a singular Gaussian vector in high dimension

Bodnar

Mazur

Muhinyuza

et al. 2020

Theor. Probability and Math. Statist.

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In this paper we consider the product of a singular Wishart random matrix and a singular normal random vector. A very useful stochastic representation is derived for this product, using which the characteristic function of the product and its asymptotic distribution under the double asymptotic regime are established. The application of obtained stochastic representation speeds up the simulation studies where the product of a singular Wishart random matrix and a singular normal random vector is present. We further document a good performance of the derived asymptotic distribution within a numerical illustration. Finally, several important properties of the singular Wishart distribution are provided.ASM Classification: 60E05, 60E10, 60F05, 62H10, 62E20

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Section: Resultsmentioning

confidence: 57%

On the product of a singular Wishart matrix and a singular Gaussian vector in high dimension

Bodnar

Mazur

Muhinyuza

et al. 2020

Theor. Probability and Math. Statist.

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“…Ledoit However, functions that depend on the product of the (inverse) Wishart random matrix and the Gaussian random vector are not comprehensively investigated in literature. Bodnar and Okhrin (2011), Bodnar et al (2013Bodnar et al ( , 2014b derived the exact distributions of the product of the (inverse) Wishart random matrix and the Gaussian random vector, which have integral representations. We note that these products have direct applications in the portfolio theory and in the discriminant analysis.…”

Section: Introductionmentioning

confidence: 99%

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

Kotsiuba

Mazur

2017

Theor. Probability and Math. Statist.

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“…In this paper we extend the results of Bodnar et al [4] by investigating the distributional properties of the product of a singular Wishart matrix and a normal vector. The singularity of the Wishart distribution leads to substantial technical complications, which have to be solved.…”

Section: Introductionmentioning

confidence: 55%

“…[3]). Bodnar et al [4] considered expressions which depend on Az, where A is a (non-singular) Wishart matrix and z is a Gaussian vector, which are independently distributed and derived a stochastic representation as well as the exact density function of LAz for an arbitrary deterministic matrix L.…”

Section: Introductionmentioning

confidence: 99%

Untitled

2015

Theor. Probability and Math. Statist.

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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.

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

Cited by 16 publications

References 9 publications

On the product of a singular Wishart matrix and a singular Gaussian vector in high dimension

On the product of a singular Wishart matrix and a singular Gaussian vector in high dimension

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

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