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Steepness In Natural Exponential Families, Afif Masmoudi
Steepness In Natural Exponential Families, Afif Masmoudi
Turkish Journal of Mathematics
The present paper studies and develops the notion of steepness in multivariate natural exponential families. Let F = \{P(m,F); m \in M_F\} be a multidimensional natural exponential family parameterized by its domain of the means M_F and let \overline{m} be an element of \partial M_F the means domain boundary. A necessary and sufficient condition for the variance function V_F is established so that the family F be steep at \overline{m} \in \partial M_F. Some characteristic properties of a steep family are given. Also, we investigate the asymptotic behaviour of a steep family F at \overline{m}.