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On the mean and dispersion of the Moore-Penrose generalized inverse of a Wishart matrix
Graduate School of Science, Hiroshima University, Japan.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering. Department of Energy and Technology, Swedish University of Agricultural Sciences, Sweden.
2019 (English)Report (Other academic)
Abstract [en]

The Moore-Penrose inverse of a singular Wishart matrix is studied. When the scale matrix equals the identity matrix the mean and dispersion matrices of the Moore-Penrose inverse are known. When the scale matrix has an arbitrary structure no exact results are available. We complement the existing literature by deriving upper and lower bounds for the expectation and an upper bound for the dispersion of the Moore-Penrose inverse. The results show that the bounds become large when the number of rows (columns) of the Wishart  matrix are close to the degrees of freedom of the distribution.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2019. , p. 12
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2019:11
Keywords [en]
Expectation and dispersion matrix, Moore-Penrose inverse, Wishart matrix
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-161722ISRN: LiTH-MAT-R-2019/11-SEOAI: oai:DiVA.org:liu-161722DiVA, id: diva2:1368548
Available from: 2019-11-07 Created: 2019-11-07 Last updated: 2019-11-07Bibliographically approved

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