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R-transform associated with asymptotic negative spectral moments of Jacobi ensemble
Linnaeus University, School of Business and Economics, Department of Economics and Statistics.
2018 (English)In: Afrika Statistika, ISSN 2316-090X, Vol. 13, no 1, p. 1531-1538Article in journal (Refereed) Published
Abstract [en]

We derive an explicit formula for the R–transform of inverse Jacobi matrix I + W^−1 W2, where W1, W2 ∼ Wp(I, ni), i = 1, 2 are independent and I is p×p dimensional identity matrix using property of asymptotic freeness of Wishart and deterministic matrices. Procedure can be extended to other sets of the asymptotically free independent matrices. Calculations are illustrated with some simulations on fixed size matrices.

Place, publisher, year, edition, pages
The Foundation of the African Society of Probability and Statistics (SPAS) , 2018. Vol. 13, no 1, p. 1531-1538
Keywords [en]
Jacobi ensemble, R-transform, S-transform, Negative spectral moments, Spectral moments, Wishart matrix, Marcenko-Pastur law, asymptotical freeness
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:lnu:diva-74379DOI: 10.16929/as/1531.118OAI: oai:DiVA.org:lnu-74379DiVA, id: diva2:1206382
Available from: 2018-05-16 Created: 2018-05-16 Last updated: 2018-05-28Bibliographically approved

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Pielaszkiewicz, Jolanta Maria

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
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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