oru.sePublikationer
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Central limit theorems for functionals of large sample covariance matrix and mean vector in matrix-variate location mixture of normal distributions
Department of Mathematics, Stockholm University, Stockholm, Sweden.
Örebro University, Örebro University School of Business. Department of Statistics.
Institute of Statistics, Leibniz University of Hannover, Hannover, Germany.
(English)Manuscript (preprint) (Other academic)
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 to 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.

Keyword [en]
Normal mixtures, skew normal distribution, large dimensional asymptotics, stochas- tic representation, random matrix theory
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:oru:diva-61246OAI: oai:DiVA.org:oru-61246DiVA: diva2:1146950
Available from: 2017-10-04 Created: 2017-10-04 Last updated: 2017-10-05Bibliographically approved

Open Access in DiVA

No full text

Search in DiVA

By author/editor
Mazur, Stepan
By organisation
Örebro University School of Business
Probability Theory and Statistics

Search outside of DiVA

GoogleGoogle Scholar

Total: 23 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf