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Mixtures of traces of Wishart and inverse Wishart matrices
Department of Economics and Statistics, Linnaeus University, Sweden; Department of Statistics, Stockholm University, Stockholm, Sweden.ORCID iD: 0000-0002-0341-7472
Department of Economics and Statistics, Linnaeus University, Sweden.
2019 (English)In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415XArticle in journal (Refereed) Epub ahead of print
Abstract [en]

AbstractTraces of Wishart matrices appear in many applications, for example in finance, discriminant analysis, Mahalanobis distances and angles, loss functions and many more. These applications typically involve mixtures of traces of Wishart and inverse Wishart matrices that are concerned in this paper. Of particular interest are the sampling moments and their limiting joint distribution. The covariance matrix of the marginal positive and negative spectral moments is derived in closed form (covariance matrix of Y=[p?1Tr{W?1},p?1Tr{W},p?1Tr{W2}]?, where W?Wp(Σ=I,n)). The results are obtained through convenient recursive formulas for E[?i=0kTr{W?mi}] and E[Tr{W?mk}?i=0k?1Tr{Wmi}]. Moreover, we derive an explicit central limit theorem for the scaled vector Y, when p/n?d<1,p,n?∞, and present a simulation study on the convergence to normality and on a skewness measure.

Place, publisher, year, edition, pages
Taylor & Francis , 2019.
Keywords [en]
covariance matrix; central limit theorem; eigenvalue distribution; inverse Wishart Matrix; Wishart matrix
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-162813DOI: 10.1080/03610926.2019.1691733ISI: 000497229800001OAI: oai:DiVA.org:liu-162813DiVA, id: diva2:1380630
Available from: 2019-12-19 Created: 2019-12-19 Last updated: 2019-12-19

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Pielaszkiewicz, Jolanta

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  • apa
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