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OPTIMAL UNBIASED MEANS, POLYNOMIAL MOMENT RELATIONS, AND NATURAL EXPONENTIAL FAMILIES

Statistics & Risk Modeling, 1996
Summary: Assume that a statistical model \({\mathcal P}\) on the real line possesses moments of every order and is such that, for some positive integer \(k\), the moment of order \(k+1\) is a polynomial function \(p\) of the \(k\) moments of lower order. Then the UMVU-property of the sample mean in a corresponding IID-model implies that \({\mathcal P}\)
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Parameterizations for Natural Exponential Families with Quadratic Variance Functions

Journal of the American Statistical Association, 1994
Abstract Parameterizations for natural exponential families (NEF's) with quadratic variance functions (QVF's) are compared according to the nearness to normality of the likelihood and posterior distribution. Nonnormality of the likelihood (posterior) is measured using two criteria.
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Real natural exponential families and generalized orthogonality

Communications in Statistics - Theory and Methods, 2023
Raouf Fakhfakh, Marwa Hamza
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Application of the variance-covariance matrix in natural exponential family to identify noise in signal

IEEE International Conference on Systems, Man and Cybernetics, 2012
Taher Ben Arab, M. Zribi, A. Masmoudi
semanticscholar   +1 more source

Functionally compatible local characteristics for some natural conjugate exponential families

2007
The local specification of priors in nondecomposable graphical models does not necessarily yield a proper joint prior for all the parameters of the model. Using results concerning general exponential families with cuts, we derive specific results for the multivariate Gamma (conjugate prior for Poisson counts) and the Wishart distribution (conjugate ...
ASCI, CLAUDIO, MAURO PICCIONI
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