Scandinavian Working Papers in Business Administration

Working Papers,
Örebro University, School of Business

No 2017:7: On the product of a singular Wishart matrix and a singular Gaussian vector in high dimensions

Taras Bodnar (), Stepan Mazur (), Stanislas Muhinyuza () and Nestor Parolya ()
Additional contact information
Taras Bodnar: Stockholm University, Postal: Department of Mathematics, Stockholm University , SE-10691 Stockholm, Sweden
Stepan Mazur: Örebro University School of Business, Postal: Örebro University, School of Business, SE - 701 82 ÖREBRO, Sweden
Stanislas Muhinyuza: Stockholm University, Postal: Department of Mathematics, Stockholm University , SE-10691 Stockholm, Sweden
Nestor Parolya: University of Hannover, Postal: Institute of Empirical Economics, Leibniz University of Hannover, D-30167 Hannover, Germany

Abstract: 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, in 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.

Keywords: singular Wishart distribution; singular normal distribution; stochastic representation; high-dimensional asymptotics

JEL-codes: C00; C13; C15

18 pages, August 22, 2017

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