Proceedings of the Japan Academy, Series A, Mathematical Sciences

On the Letac-Massam Conjecture on cones $Q_{A_{n}}$

Piotr Graczyk, Hideyuki Ishi, Salha Mamane, and Hiroyuki Ochiai

Full-text: Open access


We prove, for graphical models for nearest neighbour interactions, a conjecture stated by Letac and Massam in 2007. Our result is important in the analysis of Wishart distributions on cones related to graphical models and in its statistical applications.

Article information

Proc. Japan Acad. Ser. A Math. Sci. Volume 93, Number 3 (2017), 16-21.

First available in Project Euclid: 2 March 2017

Permanent link to this document

Digital Object Identifier

Primary: 62E15: Exact distribution theory 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 15B48: Positive matrices and their generalizations; cones of matrices 62H99: None of the above, but in this section

Laplace transform power function analysis on cones Wishart distribution graphical model


Graczyk, Piotr; Ishi, Hideyuki; Mamane, Salha; Ochiai, Hiroyuki. On the Letac-Massam Conjecture on cones $Q_{A_{n}}$. Proc. Japan Acad. Ser. A Math. Sci. 93 (2017), no. 3, 16--21. doi:10.3792/pjaa.93.16.

Export citation


  • E. Ben-David and B. Rajaratnam, The Letac-Massam conjecture and existence of high dimensional Bayes estimators for Graphical Models, arXiv:1408.0788.
  • D. M. Bressoud, Proofs and confirmations, MAA Spectrum, Math. Assoc. America, Washington, DC, 1999.
  • G. Chenevier and D. Renard, Characters of Speh representations and Lewis Caroll identity, Represent. Theory 12 (2008), 447–452.
  • P. Graczyk, H. Ishi and S. Mamane, Wishart exponential families on cones related to $A_{n}$ graphs, arXiv:1702.04065.
  • S. L. Lauritzen, Graphical models, Oxford Statistical Science Series, 17, Oxford Univ. Press, New York, 1996.
  • E. L. Lehmann and J. P. Romano, Testing statistical hypotheses, 3rd ed., Springer Texts in Statistics, Springer, New York, 2005.
  • G. Letac and H. Massam, Wishart distributions for decomposable graphs, Ann. Statist. 35 (2007), no. 3, 1278–1323.