Wishart exponential families on cones related to tridiagonal matrices

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dc.article.end-page471en_ZA
dc.article.start-page439en_ZA
dc.citation.doi10.1007/S10463-018-0647-Zen_ZA
dc.contributor.authorGraczyk, P
dc.contributor.authorIshi, H
dc.contributor.authorMamane, S
dc.date.accessioned2020-07-10T11:01:30Z
dc.date.available2020-07-10T11:01:30Z
dc.date.issued2019-04-01
dc.description.abstractLet G be the graph corresponding to the graphical model of nearest neighbor interaction in a Gaussian character. We study Natural Exponential Families (NEF) of Wishart distributions on convex cones Q G and P G , where P G is the cone of tridiagonal positive definite real symmetric matrices, and Q G is the dual cone of P G . The Wishart NEF that we construct include Wishart distributions considered earlier for models based on decomposable(chordal) graphs. Our approach is, however, different and allows us to study the basic objects of Wishart NEF on the cones Q G and P G . We determine Riesz measures generating Wishart exponential families on Q G and P G , and we give the quadratic construction of these Riesz measures and exponential families. The mean, inverse-mean, covariance and variance functions, as well as moments of higher order, are studied and their explicit formulas are given. © 2018, The Institute of Statistical Mathematics, Tokyo.en_ZA
dc.description.librarianTT2020en_ZA
dc.facultyFaculty of Scienceen_ZA
dc.identifier.citationISIen_ZA
dc.identifier.issnISSN: 0020-3157
dc.identifier.issnESSN: 1572-9052
dc.identifier.urihttps://hdl.handle.net/10539/29253
dc.journal.issue2en_ZA
dc.journal.linkhttps://hdl.handle.net/10539/28201en_ZA
dc.journal.titleAnnals of the Institute of Statistical Mathematicsen_ZA
dc.journal.volume71en_ZA
dc.language.isoenen_ZA
dc.publisherSpringer Tokyoen_ZA
dc.rights© 2018, The Institute of Statistical Mathematics, Tokyo.en_ZA
dc.schoolSchool of Statistics and Actuarial Scienceen_ZA
dc.subjectGraphical modelen_ZA
dc.subjectNearest neighbor interaction
dc.subjectWishart distribution
dc.titleWishart exponential families on cones related to tridiagonal matricesen_ZA
dc.title.alternativeANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICSen_ZA
dc.typeArticleen_ZA
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