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A property of natural exponential families in Rn with simple quadratic variance functions

โœ Scribed by V. Seshadri

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
386 KB
Volume
63
Category
Article
ISSN
0378-3758

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โœฆ Synopsis

A generalization to N" of a property of natural exponential families on ~ with simple quadratic variances is obtained. This property yields the original density in terms of the Laplace transform of the conjugate prior for the natural parameter.

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We give a characterization of the natural exponential family with quadratic variance function in terms of a discrete-time reverse martingale-like property. The proof of this result is based on the properties of the set of UMVU estimable functions.