  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 infinity such that $p/n\to c\in[0 ,
+\infty)$ when the sample covariance matrix does not need to be invertible and
$p/n\to c\in [0, 1)$ otherwise.
