Turkish Journal of Mathematics
Article Title
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
Recommended Citation
MASMOUDI, AFIF (2007) "Steepness in Natural Exponential Families," Turkish Journal of Mathematics: Vol. 31: No. 3, Article 6. Available at: https://journals.tubitak.gov.tr/math/vol31/iss3/6
