Andrew Rukhin (1993)
Applicationes Mathematicae
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The statistical estimation problem of the normal distribution function and of the density at a point is considered. The traditional unbiased estimators are shown to have Bayes nature and admissibility of related generalized Bayes procedures is proved. Also inadmissibility of the unbiased density estimator is demonstrated.
Lucien Birgé (2006)
Annales de l'I.H.P. Probabilités et statistiques
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María Del Carmen Pardo (1997)
Kybernetika
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Nicholas T. Longford (2008)
SORT
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The one-way analysis of variance is a staple of elementary statistics courses. The hypothesis test of homogeneity of the means encourages the use of the selected-model based estimators which are usually assessed without any regard for the uncertainty about the outcome of the test. We expose the weaknesses of such estimators when the uncertainty is taken into account, as it should be, and propose synthetic estimators as an alternative.
Jadwiga Kicinska-Slaby (1982)
Trabajos de Estadística e Investigación Operativa
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Lehmann in [4] has generalised the notion of the unbiased estimator with respect to the assumed loss function. In [5] Singh considered admissible estimators of function λ-r of unknown parameter λ of gamma distribution with density f(x|λ, b) = λb-1 e-λx xb-1 / Γ(b), x>0, where b is a known parameter, for loss function L(
Vassiliy G. Voinov, Mikhail S. Nikulin (1995)
Qüestiió
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Since 1956, a large number of papers have been devoted to Stein's technique of obtaining improved estimators of parameters, for several statistical models. We give a brief review of these papers, emphasizing those aspects which are interesting from the point of view of the theory of unbiased estimation.