Quadratic and inverse regressions for Wishart distributions

Annals of Statistics

Volumn 26, Issue 2, 1998, Pages 573-595

  Letac, Gérard ^a   Massam, Hélène ^b,c  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

^b YORK UNIVERSITY   (Canada)

^c UNIVERSITY OF VIRGINIA   (United States)

Author keywords

conditional moments; Jordan algebras; Natural exponential families; Wishart distributions

Indexed keywords

EID: 0032344430     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1028144849     Document Type: Article

References (18)

1. CASALIS, M. (1990). Familles exponentielles naturelles invariantes par un groupe. Thèse, Univ. Paul Sabatier.
2. CASALIS, M. (1992). Un estimateur de la variance pour une famille exponentielle à fonction variance quadratique. C.R. Acad. Sci. Paris Sér. I, Math. 314 143-146.
3. CASALIS, M. and LETAC, G. (1996). The Lukacs-Olkin-Rubin characterization of the Wishart distributions on symmetric cones. Ann. Statist. 24 763-786.
4. DAS GUPTA, S. (1968). Some aspects of discrimination function coefficients. Sankhyā Ser. A 30 387-400.
5. FARAUT, J. and KORANYI, A. (1994). Analysis on Symmetric Cones. Oxford Univ. Press.
6. HUANG, W.-J., LI, S.-H. and HUANG, M.-N. L. (1994). Characterizations of the Poisson process as a renewal process via two conditional moments. Ann. Inst. Statist. Math. 46 351-360.
7. KAWATA, Y. (1972). Fourier Analysis and Probability. Wiley, New York.
8. LETAC, G. and MASSAM, H. (1997). Representations of an exponential dispersion model (with an appendix by E. Neher). Technical report, Univ. Paul Sabatier.
9. LUKACS, E. (1955). A characterization of the gamma distribution. Ann. Math. Statist. 26 319-324.
10. 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. Statist. 22 369-394.
11. MASSAM, H. and NEHER, E. (1997). On transformations and determinants of Wishart variables on symmetric cones. J. Theoret. Probab. 10 867-902.
12. MUIRHEAD, R. (1982). Aspects of Multivariate Analysis. Wiley, New York.
13. OLKIN, I. and RUBIN, H. (1962). A characterization of the Wishart distribution. Ann. Math. Statist. 33 1272-1280.
14. RAO, C. R. (1948). On a problem of Ragnar Frish. Econometrica 15 245-249.
15. SRIVASTAVA, M. S. (1965). On complex Wishart distribution. Ann. Math. Statist. 36 313-317.
16. VON ROSEN, D. (1988). Moments for the inverted Wishart distribution. Scaned. J. Statist. 15 97-109.
17. WANG, F. (1981). Extensions of Lukacs' characterization of the gamma distribution. Analytic Methods in Probability Theory. Lecture Notes in Math. 861 166-177. Springer, New York.
18. WESOŁOWSKI, J. (1990). A constant regression characterization of the gamma law. Adv. in Appl. Probab. 22 488-489.