Steepness in Natural Exponential Families

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}.

Anahtar Kelimeler:

Convex, natural exponential family, face, means domain, steep, variance function

Steepness in Natural Exponential Families

Keywords:

Convex, natural exponential family, face, means domain, steep, variance function,

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Laboratoire de Probabilit´e et Statistiques. Universit´e de Sfax. Facult´e des Sciences, B.P 802, Sfax-TUNISIA e-mail: AŞf.Masmoudi@fss.rnu.tn