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Turkish Journal of Mathematics

Authors

AFIF MASMOUDI

DOI

-

Abstract

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}.

First Page

319

Last Page

331

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