# Lund University Publications

## LUND UNIVERSITY LIBRARIES

### Central limit theorems for functionals of large dimensional sample covariance matrix and mean vector in matrix-variate skewed model

(2016) In Working Papers in Statistics
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 general skew normal distribution. 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 an inverse 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 sample size n approach to infinity such that p/n → c ∈ (0, 1).
author
organization
publishing date
type
Working Paper
publication status
published
subject
keywords
Skew normal distribution, large dimensional asymptotics, stochastic representation, random matrix theory
in
Working Papers in Statistics
issue
2016:4
pages
28 pages
publisher
Department of Statistics, Lund university
language
English
LU publication?
yes
id
fa6bc35e-1045-4b06-a3f2-a7bdea8d8b13
2016-09-21 12:54:47
date last changed
2016-09-21 12:54:47
```@misc{fa6bc35e-1045-4b06-a3f2-a7bdea8d8b13,
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 general skew normal distribution. 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 an inverse 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 sample size n approach to infinity such that p/n → c ∈ (0, 1).},
author       = {Bodnar, Taras and Mazur, Stepan and Parolya, Nestor},
keyword      = {Skew normal distribution,large dimensional asymptotics,stochastic representation,random matrix theory},
language     = {eng},
number       = {2016:4},
pages        = {28},
publisher    = {ARRAY(0x79d3ce0)},
series       = {Working Papers in Statistics},
title        = {Central limit theorems for functionals of large dimensional sample covariance matrix and mean vector in matrix-variate skewed model},
year         = {2016},
}

```