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

José A. Díaz-García, Ramón Gutierrez Jáimez and Kanti V. Mardia

Journal of Multivariate Analysis, 1997, vol. 63, issue 1, 73-87

Abstract: 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.

Keywords: singular; matrix; distributions; Wishart; distribution; Pseudo-Wishart; distribution; Normal; matrix; variate; distribution; Noncentral; distributions; singular; values; Stiefel; manifold; shape; size-and-shape (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (23)

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