On Transformations and Determinants of Wishart Variables on Symmetric Cones

Journal of Theoretical Probability

Volumn 10, Issue 4, 1997, Pages 867-902

  Massam, Hélène ^a   Neher, Erhard ^b  

^a YORK UNIVERSITY   (Canada)

^b UNIVERSITY OF OTTAWA   (Canada)

Author keywords

Determinants; Symmetric cones; Wishart distributions

Indexed keywords

EID: 0031511976     PISSN: 08949840     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022658415699     Document Type: Article

References (20)

1. Andersen, H. H., Højbjerre, M., Sørensen, D., and Eriksen, P. S. (1995). Linear and Graphical Models for the Multivariate Complex Normal Distribution, Springer Verlag, Lecture Notes in Statistics.
2. Andersson, S. A., and Perlman, M. D. (1995). Unbiasedness of the likelihood ratio test for lattice conditional independence models, J. Mult. Anal. 53, 1-17.
3. Braun, H., and Koecher, M. (1966). Jordan Algebren, Springer Verlag, Berlin-Heidelberg.
4. Casalis, M. (1990). Familles exponentielles naturelles invariantes par un groupe, Thesis, Université Paul Sabatier, Toulouse, France.
5. Casalis, M., and Letac, G. (1994). Characterization of the Jorgensen set in generalized linear models, Test 3, 145-162.
6. Faraut, J., and Koranyi, (1994). Analysis and Symmetric Cones, Oxford University Press.
7. Gindikin, S. G. (1994). Invariant Generalized Functions in Homogeneous Domains, J. Funct. Anal. Appl. 9, 50-52.
8. Jacobson, N. (1968). Structure and Representations of Jordan Algebras, Amer. Math. Soc. Coll. Publ. XXXIX, Providence, Rhode Island.
9. Jensen, S. T. (1988). Covariance hypotheses which are linear in both the covariance and the inverse covariance, Ann. of Statist. 16, 302-322.
10. Koecher, M. (1983). Lineare Algebra und Analytische Geometrie, Vol. 2, Grundwissen Mathematik, Springer Verlag.
11. Krishnaiah, P. R. (1976). Some recent developments on complex multivariate distributions, J. Mult. Anal. 6, 1-30.
12. Lauritzen, S. L. (1996). Graphical Models, Clarendon Press, Oxford.
13. Letac, G. (1994). Les Familles Exponentielles Statistiques Invariantes par les Groupes du Cone et du Paraboloide de Révolution [Volume in honor of Takacs, L., Galambos, J., and Gani J. eds.].
14. Letac, G., and Massam H. (1995). Craig's Theorem for the Wishart Distribution on Symmetric Cones, Ann. Inst. Stat. Math. 47, 785-799.
15. Loos, O. (1989). On the Socle of a Jordan Pair, Collect. Math. 40, 109-125.
16. Loos, O. (1991). Finiteness Conditions in Jordan Pairs, Math. Z. 206, 577-587.
17. Massam, H. (1994). An Exact Decomposition Theorem and a Unified View of Some Related Distributions for a Class of Exponential Transformation Models on Symmetric Cones, Ann. of Statist. 22, 369-393.
18. Massam, H., and Neher, E. (1996). Lattice Conditional Independence Models with Covariance Matrices in Symmetric Cones (submitted for publication).
19. Muirhead, R. J. (1982). Aspects of Multivariate Statistical Theory, Wiley, New York.
20. 2, t, and F Fields, Adv. Appl. Prob. 26, 13-42.