Abstract
Exponential dispersion models (EDMs) with unknown mean and dispersion parameters are studied with respect to second-order minimax estimation of the mean, for a nonrestricted space of mean values. A modified second-order minimax estimator is presented and some of its asymptotic properties are established. In particular, we provide some necessary and sufficient conditions for such modified estimators to improve on the sample mean. The present results extend those of Landsman [Second order minimax estimation of the mean value for exponential dispersion models. J. Statist. Plann. Inference, 98, 57-71, 2001.] which were given for EDMs with a known dispersion parameter. Applications to the Tweedie class with the power parameter γ, 2 ≤ γ ≤ ∞, are presented.
| Original language | English |
|---|---|
| Pages (from-to) | 3837-3851 |
| Number of pages | 15 |
| Journal | Journal of Statistical Planning and Inference |
| Volume | 136 |
| Issue number | 11 |
| DOIs | |
| State | Published - 1 Nov 2006 |
Keywords
- Exponential dispersion model
- Generalized Bayes estimator
- Natural exponential family
- Second-order minimaxity
- Tweedie class
- Variance function
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics