An order- exponential family is minimal if no nonzero linear combination of its canonical sufficient statistics is almost surely constant under the base measure. Equivalently, its sufficient-statistic support lies in no proper affine hyperplane. Its cumulant function then has positive-definite Hessian matrix on the interior natural domain, because that Hessian is a covariance matrix.
Articles by others on the same topic
There are currently no matching articles.