The Wishart Distribution on Symmetric ConesShow others and affiliations
2023 (English)In: Non-commutative and Non-associative Algebra and Analysis Structures: SPAS 2019, Västerås, Sweden, September 30 - October 2 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Springer , 2023, p. 661-684Conference paper, Published paper (Refereed)
Abstract [en]
In this paper we discuss the extension of the Wishart probability distributions in higher dimension based on the boundary points of the symmetric cones in Jordan algebras. The symmetric cones form a basis for the construction of the degenerate and non-degenerate Wishart distributions in the field of Herm(m,C), Herm(m,H), Herm(3,O) that denotes respectively the Jordan algebra of all Hermitian matrices of size m× m with complex entries, the skew field H of quaternions, and the algebra O of octonions. This density is characterised by the Vandermonde determinant structure and the exponential weight that is dependent on the trace of the given matrix.
Place, publisher, year, edition, pages
Springer , 2023. p. 661-684
Series
Springer Proceedings in Mathematics and Statistics, ISSN 21941009 ; 426
Keywords [en]
Vandermonde determinant, Jordan algebra, Symmetric cone, Wishart distribution
National Category
Probability Theory and Statistics Algebra and Logic Mathematical Analysis
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-64593DOI: 10.1007/978-3-031-32009-5_23Scopus ID: 2-s2.0-85174443553ISBN: 9783031320088 (print)OAI: oai:DiVA.org:mdh-64593DiVA, id: diva2:1808055
Conference
International Conference on Stochastic Processes and Algebraic Structures—From Theory Towards Applications, SPAS 2019, Västerås, Sweden, 30 September - 2 October 2019
2023-10-302023-10-302023-12-27Bibliographically approved