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 -