Journals / Turkish Journal of Mathematics / 2007 / Cilt: 31 - Sayı: 3
Steepness in Natural Exponential Families
- Pages
- 319–331
- DOI
- —
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}.
Özet
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}.