Wishart and Pseudo-Wishart Distributions and Some Applications to Shape Theory
Suppose thatX~N-m([mu],Â [Sigma],Â [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 ) is expanded for the singular value decomposition of a matrixZof orderN-mwhen the rank (Z)=q[less-than-or-equals, slant]min(N,Â 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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Volume (Year): 63 (1997)
Issue (Month): 1 (October)
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- 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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