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On the Letac-Massam conjecture on cones \(Q_{A_n}\). (English) Zbl 1422.62067

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.

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

Citations:

Zbl 1194.62078
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