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Wishart and Pseudo-Wishart Distributions and Some Applications to Shape Theory

  • Díaz-García, José A.
  • Jáimez, Ramón Gutierrez
  • Mardia, Kanti V.
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    Suppose thatX~N-m([mu], [Sigma], [Theta]). An expression for the density function is given when[Sigma][greater-or-equal, slanted]0 and/or[Theta]:[greater-or-equal, slanted]0. An extension of Uhlig's result (Uhlig [17]) is expanded for the singular value decomposition of a matrixZof orderN-mwhen the rank (Z)=q[less-than-or-equals, slant]min(N, m). This paper fills an important gap in unifying, for the first time, all Wishart and pseudo-Wishart distributions, whether central or noncentral, whether singular or nonsingular, and applying them in shape analysis. In particular, the shape density and the size-and-shape cone density are obtained for the singular general case.

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 63 (1997)
    Issue (Month): 1 (October)
    Pages: 73-87

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    Handle: RePEc:eee:jmvana:v:63:y:1997:i:1:p:73-87
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    1. Goodall, Colin & Mardia, Kanti V., 1992. "The noncentral Bartlett decompositions and shape densities," Journal of Multivariate Analysis, Elsevier, vol. 40(1), pages 94-108, January.
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