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

Authors

  • Igor Kotsiuba Department of Probability Theory and Statistics Ivan Franko National University of Lviv Universitetska 1, Lviv
  • Stepan Mazur Department of Statistics, Lund University, PO Box 742, SE_22007 Lund

Keywords:

Wishart distribution, multivariate normal distribution, integral approximation

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 its approximate density function formula which is based on the

Gaussian integral and the third order Taylor expansion. Furthermore, we compare

obtained asymptotic and approximate density functions with the exact density which

is obtained by Bodnar and Okhrin (2011). A good performance of obtained results

is documented in the numerical study.

Author Biography

Stepan Mazur, Department of Statistics, Lund University, PO Box 742, SE_22007 Lund

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 its approximate density function formula which is based on the Gaussian integral and the third order Taylor expansion. Furthermore, we compare obtained asymptotic and approximate density functions with the exact density which is obtained by Bodnar and Okhrin (2011). A good performance of obtained results is documented in the numerical study.

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Issue

2015

Section

Working Papers in Statistics