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Identifiability of differentiable bayes estimators of the uniform scale parameter

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  • Lillo Rodríguez, Rosa Elvira

Abstract

The problem of estimating the uniform scale parameter under the squared error loss function is investigated from a Bayesian viewpoint. A complete characterization of differentiable Bayes estimators and generalized Bayes estimators is given. The solution determines a family of prior measures both proper and improper, involving densities whose support is the whole parameter space, i.e, the interval (0,00)' Relations between degrees of smoothness of the estimators and the priors are investigated. We will also consider sequences, depending on the sample size, of Bayes (generalized Bayes) estimators with a fixed structure which are generated from a unique prior measure. They will be named strong Bayes sequences or strong generalized Bayes sequences. We characterize this type of Bayes estimation which is more restrictive than the usual one. As a consequence oithe characterization results, we will prove that strong Bayes sequences of polynomial form are not possible for the uniform scale parameter. Moreover we will show that the sequence whose components are the minimum risk equivariant estimator for each sample size is the best strong generalized Bayes sequence of polynomial form.

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  • Lillo Rodríguez, Rosa Elvira, 2000. "Identifiability of differentiable bayes estimators of the uniform scale parameter," DES - Working Papers. Statistics and Econometrics. WS 9857, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:9857
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    1. Theofanis Sapatinas, 1995. "Identifiability of mixtures of power-series distributions and related characterizations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 447-459, September.
    2. Arjun Gupta & Jacek Wesolowski, 1997. "Uniform Mixtures Via Posterior Means," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 171-180, March.
    3. Wesolowski, J., 1995. "Bivariate Discrete Measures via a Power Series Conditional Distribution and a Regression," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 219-229, November.
    4. Lillo R. E. & Martín M., 1999. "Characterization Of Bayes Estimators Of The Uniform Scale Parameter," Statistics & Risk Modeling, De Gruyter, vol. 17(1), pages 31-48, January.
    5. Papageorgiou, H. & Wesolowski, Jacek, 1997. "Posterior mean identifies the prior distribution in nb and related models," Statistics & Probability Letters, Elsevier, vol. 36(2), pages 127-134, December.
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