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Central limit theorems for functionals of large sample covariance matrix and mean vector in matrix-variate location mixture of normal distributions

Taras Bodnar (), Stepan Mazur () 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
Stepan Mazur: Örebro University School of Business, Postal: Örebro University, School of Business, SE - 701 82 ÖREBRO, Sweden, https://www.oru.se/personal/stepan_mazur

No 2017:5, Working Papers from Örebro University, School of Business

Abstract: In this paper we consider the asymptotic distributions of functionals of the sample covariance matrix and the sample mean vector obtained under the assumption that the matrix of observations has a matrix-variate location mixture of normal distributions. The central limit theorem is derived for the product of the sample covariance matrix and the sample mean vector. Moreover, we consider the product of the inverse sample covariance matrix and the mean vector for which the central limit theorem is established as well. All results are obtained under the large-dimensional asymptotic regime where the dimension p and the sample size n approach to in nity such that p=n ! c 2 [0;+1) when the sample covariance matrix does not need to be invertible and p=n ! c 2 [0; 1) otherwise.

Keywords: Normal mixtures; skew normal distribution; large dimensional asymptotics; stochastic representation; random matrix theory (search for similar items in EconPapers)
JEL-codes: C00 C13 C15 (search for similar items in EconPapers)
Pages: 30 pages
Date: 2017-08-22
New Economics Papers: this item is included in nep-ecm
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Related works:
Journal Article: Central limit theorems for functionals of large sample covariance matrix and mean vector in matrix‐variate location mixture of normal distributions (2019) Downloads
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