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

Taras Bodnar (taras.bodnar@math.su.se), Stepan Mazur, Stanislas Muhinyuza (stanislas.muhinyuza@math.su.se) and Nestor Parolya
Additional contact information
Taras Bodnar: Stockholm University, Postal: Department of Mathematics, Stockholm University , SE-10691 Stockholm, Sweden, http://www.su.se/profiles/tbodn-1.219689
Stanislas Muhinyuza: Stockholm University, Postal: Department of Mathematics, Stockholm University , SE-10691 Stockholm, Sweden

No 2017:7, Working Papers from Örebro University, School of Business

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 (search for similar items in EconPapers)
JEL-codes: C00 C13 C15 (search for similar items in EconPapers)
Pages: 18 pages
Date: 2017-08-22
New Economics Papers: this item is included in nep-ecm and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:hhs:oruesi:2017_007

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