TY - JOUR

T1 - Central limit theorems for functionals of large sample covariance matrix and mean vector in matrix-variate location mixture of normal distributions

AU - Bodnar, Taras

AU - Mazur, Stepan

AU - Parolya, Nestor

PY - 2019/6/1

Y1 - 2019/6/1

N2 - 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 infinity such that p/n→c ∈ [0, + ∞) when the sample covariance matrix does not need to be invertible and p/n→c ∈ [0,1) otherwise.

AB - 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 infinity such that p/n→c ∈ [0, + ∞) when the sample covariance matrix does not need to be invertible and p/n→c ∈ [0,1) otherwise.

KW - large-dimensional asymptotics

KW - normal mixtures

KW - random matrix theory

KW - skew normal distribution

KW - stochastic representation

UR - http://www.scopus.com/inward/record.url?scp=85061927074&partnerID=8YFLogxK

U2 - 10.1111/sjos.12383

DO - 10.1111/sjos.12383

M3 - Article

AN - SCOPUS:85061927074

VL - 46

SP - 636

EP - 660

JO - Scandinavian Journal of Statistics: theory and applications

JF - Scandinavian Journal of Statistics: theory and applications

SN - 0303-6898

IS - 2

ER -