Conjugate Priors for Exponential Families Having Quadratic Variance Functions
โ Scribed by Consonni, Guido; Veronese, Piero
- Book ID
- 120258095
- Publisher
- American Statistical Association
- Year
- 1992
- Tongue
- English
- Weight
- 482 KB
- Volume
- 87
- Category
- Article
- ISSN
- 0162-1459
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๐ SIMILAR VOLUMES
Within the framework of the quadratic natural exponential families we construct a basis of polynomials orthogonal with respect to the posterior density. This construction is adapted from Walter and Hamedani (Ann. Statist. 3 (1991) 1191) and we exploit them to establish lower bounds for the posterior
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.
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.