Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/244527 
Year of Publication: 
2017
Series/Report no.: 
Working Paper No. 5/2017
Publisher: 
Örebro University School of Business, Örebro
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.
Subjects: 
Normal mixtures
skew normal distribution
large dimensional asymptotics
stochastic representation
random matrix theory
JEL: 
C00
C13
C15
Document Type: 
Working Paper

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