Reference priors for exponential families with simple quadratic variance function

Reference priors for exponential families with increasing dimension

In this article, we establish the asymptotic normality of the posterior distribution for the natural parameter in an exponential family based on independent and identically distributed data. The mode of convergence is expected Kullback-Leibler distance and the number of parameters p is increasing with the sample size n. Using this, we give an asymptotic expansion of the Shannon mutual informati...

Conjugate Priors for Exponential Families Having Cubic Variance Functions

In this paper, we give three equivalent properties of the class of multivariate simple cubic natural exponential families (NEF’s). The first property says that the cumulant function of any basis of the family is a solution of some Monge-Ampère equation, the second is that the variance function satisfies a differential equation, and the third is characterized by the equality between two families...

Natural Exponential Families with Polynomial Variance Function and Umbral Calculus

In this paper we use the Umbral Calculus to investigate the relation between natural exponential families and Sheeer polynomials. We give a new proof for the classiication of univariate natural exponential families with quadratic variance function. We also show how our methods apply to natural exponential families with variance function of any order and to multivariate natural exponential famil...

Posterior Normality and Reference Priors for Exponential Families with Increasing Dimension

In this article, we study asymptotic normality of the posterior distribution of the natural parameter in an exponential family based on independent and identically distributed (i.i.d.) data, that is, in terms of expected Kullback-Leibler divergence, when the number of parameters p is increasing with the sample size n. We use this to generate an asymptotic expansion of the Shannon mutual informa...

Quadratic Hermite-Padé polynomials associated with the exponential function