Scandinavian Working Papers in Economics
Working Papers,
Örebro University, School of Business
No 2017:5: 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
Stepan Mazur: Örebro University School of Business, Postal: Örebro University, School of Business, SE - 701 82 ÖREBRO, Sweden
Nestor Parolya: Institute of Statistics, Leibniz University of Hannover, Postal: Institute of Statistics, Leibniz University of Hannover, D-30167 Hannover, Germany
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
30 pages, August 22, 2017
Full text files
wp-5-2017.pdf
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