Steepness in Natural Exponential Families
Authors : Afif Masmoudi
Pages : 319-331
View : 7 | Download : 6
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :The present paper studies and develops the notion of steepness in multivariate natural exponential families. Let F = \{P(m,F); m \in MF\} be a multidimensional natural exponential family parameterized by its domain of the means MF and let \overline{m} be an element of \partial MF the means domain boundary. A necessary and sufficient condition for the variance function VF is established so that the family F be steep at \overline{m} \in \partial MF. Some characteristic properties of a steep family are given. Also, we investigate the asymptotic behaviour of a steep family F at \overline{m}.Keywords : Convex, natural exponential family, face, means domain, steep, variance function