Wishart Distributions on Homogeneous Cones

Anderson, T. W. (1984). An Introduction to Multivariate Statistical Analysis, 2nd ed., Wiley, New York. Anderson, T. W. (1969). Statistical inference for covariance matrices with linear structure. In Proc.Second Internat.Symp.Multivariate Anal. In Krishnaiah, P. R. (ed.), Academic, New York. pp. 55–66. Anderson, T. W. (1970). Estimation of covariance matrices which are linear combinations or whose inverses are linear combinations of given matrices. In Essays in Probability and Statistics. (Bose, R. C., Chakravati, I. M., Mahalanobis, P. C., Rao, C. R. and Smith, K. J. C. eds.), 1–24. Univ. North Carolina Press, Chapel Hill. Anderson, T. W. (1973). Asymptotically efficient estimation of covariances with linear structure. Ann.Stat. 1, 135–141. Andersson, S. A. (1975). Forelæsningsnoter i. erdimensional statististisk analyse. Lecture notes. Inst. Mathematical Statistics, Univ. Copenhagen. (In Danish). Andersson, S. A. (1975). Invariant normal models. Ann.Stat. 3, 132–154. Andersson, S. A. (1976). Forelæsningsnoter i. erdimensional statististisk analyse. Lecture notes, Inst. Mathematical Statistics, Univ. Copenhagen. (In Danish). Andersson, S. A. (1978). On the mathematical foundation of multivariate statistical analysis. Lecture Notes presented in Lunteren, Holland, Nov. 1978, Inst. Mathematical Statistics. Univ. Copenhagen. Andersson, S. A. (1992). Normal linear models given by group symmetry. Lecture Notes presented at the DMW-Seminar Guntzburg, Germany. Inst. Mathematical Statistics, Univ. Copenhagen. Andersson, S. A. (2004). Hypothesis testing for the general Wishart distribution on homogeneous cones. In preparation. Andersson, S. A., Brøns, H. K., and Tolver Jensen, S. (1975). En algebraisk teori for normale statistiske modeller. Inst. Mathematical Statistics, Univ. Copenhagen. (In Danish). Andersson, S. A., Brøns, H. K., and Tolver Jensen, S. (1983). Distribution of Eigenvalues in multivariate statistical analysis. Ann.Stat. 11, 392–415. Andersson, S. A., Madigan, D., Perlman, M. D., and Triggs, C. M. (1995). On the relation between conditional independence models determined by nite distributive lattice and directed acyclic graphs. J.Stat.Plan.Inference 48, 25–46. Andersson, S. A., Madigan, D., Perlman, M. D., and Triggs, C. M. (1997). A graphical characterization of lattice conditional independence models. Artif.Intell. 21, 27–50. Andersson, S. A., and Madsen, J. (1998). Symmetry and lattice conditional independence in a multivariate normal distribution. Ann.Stat. 26, 525–572. Andersson, S. A., and Perlman, M. D. (1993). Lattice models for conditional independence in a multivariate normal distribution. Ann.Stat. 21, 1318–1358. Andersson, S. A., and Perlman, M. D. (1994). Normal linear models with lattice conditional independence restrictions. Multivariate Anal.Appl. 24, 97–110. Andersson, S. A., Madigan, D., and Perlman, M. D. (2001). Alternative Markov properties for chain graphs. Scand.J.Stat. 28, 33–85. Andersson, S. A., Letac, G., and Massam, H. (2004). The variance of the Wishart distributions on homogeneous cones. In preparation. Andersson, S. A., and Wojnar G. G. (2004). The Wishart Distribution on Homogeneous Cones. Acta et Commentstiones Universitatis Tartuensis de Mathematica 8. To appear. Andersson, S. A., and Sherrer, C. (2004). The multivariate circular symmetry model. In preparation. Arnold, S. F. (1973). Application of the theory of products of certain patterned covariance matrices. Ann.Stat. 1, 682–699. Baez, J. C. (2002). The octonions. Bull.Amer.Math.Soc. 39 (2)145–205. Barndorff-Nielsen, O. (1978). Information and Exponential Families in Statistical Theory, Wiley, New York. Bourbaki, N. (1963). ´El ´ements de Math ´ematique. Integration, Ch. 7 à 8. Hermann, Paris. Bourbaki, N. (1971). ´El ´ements de Math ´ematique. Topologie G ´en ´erale. Ch. 1 à 4. Hermann, Paris. Brøns, H. K. (1969). Forelæsningsnoter i den normale fordelings teori. Personal communication, Inst. Mathematical Statistics, Univ. Copenhagen. (In Danish). Brøns, H. K. (1998). Flerdimensional statistisk analyse. Manuscript. Dept. of Mathematical Statistics, Univ. Copenhagen. (In Danish). Casalis, M. (1991). Les families exponentielles ´a variance quadratique homogène sont de lois de Wishart sur un cone sym ´etrique. C.R.Acad.Sci.Paris S ´er.I Math. 312, 537–540. Casalis, M., and Letac, G. (1996). The Lukacs-Olkin-Rubin characterization of the Wishart distribution on symmetric cones. Ann.Stat. 24, 763–786. Castelo, R., and Siebes, A. (2003). A characterization of moral transitive acyclic graphs Markov models as labeled trees. J. Stat.Plann.Inference 115, 235–259. Faraut, J., and Kor ´anyi, A. (1994). Analysis on Symmetric Cones. Oxford University Press, New York. Goodman, N. R. (1963). Statistical analysis based on certain multivariate complex distributions. Ann.Math.Stat. 34, 152–176. Jacobson, N. (1968). Structure and Representations of Jordan Algebras. Amer. Math. Soc., Providence, R. I. Jensen, J. L. (1991). A large deviation-type approximation for the “Box class ”of likelihood ratio criteria. J.Amer.Stat.Assoc. 86, 437–440. Khatri, C. G. (1965a). Classical statistical analysis based on a certain multivariate complex Gaussian distribution. Ann.Math.Stat. 36, 98–114. Khatri, C. G. (1965b). A test of reality of a covariance matrix in certain complex Gaussian distributions. Ann.Math.Stat. 36, 115–119. Lauritzen, S. L. (1996). Graphical Models. Oxford University Press, Oxford. Letac, G., and Massam, H. (1998). Quadratic and inverse regression for the Wishart distribution. Ann.Stat. 26, 573–595. Letac, G., and Massam, H. (2000). Representations of the Wishart distributions. Contemp.Math. 261, 121–142. Massam, H., and Neher, E. (1997). On transformations and determinants of Wishart variables on symmetric cones. J.Theoret.Prob. 10, 867–902. Olkin, I., and Press, S. J. (1969). Testing and estimation for a circular stationary model. Ann.Math.Stat. 40, 1358–1373. Olkin, I. (1973). Testing and estimation for structures which are circularly symmetric in blocks. Proc.Res.Sem.Multivariate Statistical Inference. Dalhousie.Nova Scotia, North Holland, Amsterdam, pp. 183–195. Perlman, M. D. (1987). Group symmetry covariance models. Stat.Sci. 2, 421–425. Seely, J. (1971). Quadratic subspaces and completeness. Ann.Math.Stat. 42, 710–721. Seely, J. (1972). Completeness for a family of multivariate normal distributions. Ann.Math.Stat. 43, 1644–1647. Sherrer, C. (2003). Multivariate circular symmetry models. Ph.D.Thesis, Indiana University. Tolver Jensen, S. (1973). Forelæsninger i matematisk statistik. Lecture notes, Inst. Mathematical Statistics, Univ. Copenhagen. (In Danish.) Tolver Jensen, S. (1974). Forelæsningsnoter. erdimensional statistisk analyse. Lecture notes, Inst. Mathematical Statistics, Univ. Copenhagen. (In Danish.) Tolver Jensen, S. (1977). Flerdimensional statistisk analyse. Lecture notes, Inst. Mathematical Statistics, Univ. Copenhagen. (In Danish.) Tolver Jensen, S. (1983). Symmetrimodeller. Lecture notes. Inst. Mathematical Statistics. Univ. Copenhagen. (In Danish.). Tolver Jensen, S. (1988). Covariance hypotheses which are linear in both the covariance and the inverse covariance. Ann.Stat. 16, 302–322. Vinberg, E. B. (1960). Homogeneous cones. Dokl.Akad.Nauk SSSR. 133, 9–12; Soviet Math.Dokl. 1, 787–790. Vinberg, E. B. (1962). Automorphisms of homogeneous convex cones. Dokl.Akad.Nauk SSSR. 143, 265–268; Soviet Math.Dokl. 3, 371–374. Vinberg, E. B. (1963). The theory of convex homogeneous cones. Trudy Moskov.Mat.Obsc. 12, 303–358; Trans.Moscow Math.Soc. 12, 340–403. Vinberg, E. B. (1965). The structure of the group of automorphisms of a homogeneous convex cone. Trudy Moskov.Mat.Obsc. 13, 56–83; Trans.Moskow Math.Soc. 13, 63–93. Wishart, J. (1928). The generalized product moment distribution in a sample from a normal multivariate population. Biometrika 20A, 32–52. Votaw, D. F. (1948). Testing compound symmetry in a normal multivariate distribution. Ann.Math.Stat. 19, 447–473. Wilks, S. S. (1946). Sample criteria for testing equality of means, equality of variances, and equality of covariances in a normal multivariate distribution. Ann.Math.Stat. 17, 257–281. Wojnar, G. G. (2000). Generalized Wishart models on convex homogeneous cones, Ph.D.Thesis. Indiana University.