Graczyk, Piotr; Ishi, Hideyuki; Mamane, Salha; Ochiai, Hiroyuki On the Letac-Massam conjecture on cones \(Q_{A_n}\). (English) Zbl 1422.62067 Proc. Japan Acad., Ser. A 93, No. 3, 16-21 (2017). Summary: We prove, for graphical models for nearest neighbour interactions, a conjecture stated by G. Letac and H. Massam [Ann. Stat. 35, No. 3, 1278–1323 (2007; Zbl 1194.62078)]. Our result is important in the analysis of Wishart distributions on cones related to graphical models and in its statistical applications. Cited in 2 Documents MSC: 62E15 Exact distribution theory in statistics 42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 15B48 Positive matrices and their generalizations; cones of matrices 05C90 Applications of graph theory 44A10 Laplace transform 62H05 Characterization and structure theory for multivariate probability distributions; copulas Keywords:Laplace transform; power function; analysis on cones; Wishart distribution; graphical model Citations:Zbl 1194.62078 PDFBibTeX XMLCite \textit{P. Graczyk} et al., Proc. Japan Acad., Ser. A 93, No. 3, 16--21 (2017; Zbl 1422.62067) Full Text: DOI