WISHART AND PSEUDO-WISHART DISTRIBUTIONS AND SOME APPLICATIONS TO SHAPE-THEORY

Citation
Ja. Diazgarcia et al., WISHART AND PSEUDO-WISHART DISTRIBUTIONS AND SOME APPLICATIONS TO SHAPE-THEORY, Journal of Multivariate Analysis, 63(1), 1997, pp. 73-87
Citations number
17
Categorie Soggetti
Statistic & Probability","Statistic & Probability
ISSN journal
0047259X
Volume
63
Issue
1
Year of publication
1997
Pages
73 - 87
Database
ISI
SICI code
0047-259X(1997)63:1<73:WAPDAS>2.0.ZU;2-I
Abstract
Suppose that X similar to N-N x m(mu, Sigma, Theta). An expression for the density function is given when Sigma greater than or equal to 0 a nd/or Theta greater than or equal to 0. An extension of Uhlig's result (Uhlig [17]) is expanded for the singular value decomposition of a ma trix Z of order N x m when the rank (Z) = q less than or equal to min( N, m). This paper fills an important gap in unifying, for the first ti me, all Wishart and pseudo-Wishart distributions, whether central or n oncentral, whether singular or nonsingular, and applying them in shape analysis. In particular, the shape density and the size-and-shape con e density are obtained for the singular general case. (C) 1997 Academi c Press.