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Central limit theorems for functionals of large sample covariance matrix and mean vector in matrix-variate location mixture of normal distributions
Stockholm University, Faculty of Science, Department of Mathematics.ORCID iD: 0000-0001-7855-8221
Number of Authors: 32019 (English)In: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 46, no 2, p. 636-660Article in journal (Refereed) Published
Abstract [en]

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 is an element of [0, + infinity) when the sample covariance matrix does not need to be invertible and p/n -> c is an element of [0,1) otherwise.

Place, publisher, year, edition, pages
2019. Vol. 46, no 2, p. 636-660
Keywords [en]
large-dimensional asymptotics, normal mixtures, random matrix theory, skew normal distribution, stochastic representation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-169237DOI: 10.1111/sjos.12383ISI: 000465606900012OAI: oai:DiVA.org:su-169237DiVA, id: diva2:1326316
Available from: 2019-06-18 Created: 2019-06-18 Last updated: 2019-06-18Bibliographically approved

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Bodnar, TarasParolya, Nestor
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