Estimation of Bounded Location and Scale Parameters
AbstractWhen a location parameter is restricted to a bounded interval, the paper addresses the issue of deriving estimators improving on the best location equivariant (or Pitman) estimator under the squared error loss. A class of improved estimators is constructed, and it is verified that the Bayes estimator against the uniform prior over the bounded interval and the truncated estimator belongs to the class. When a symmetric density is considered for the location family, the paper obtains sufficient conditions on hte density under which the class includes the Bayes estimators with respect to the two-point boundary symmetric prior and general continuous prior distributions. It is demonstrated that the conditions on the symmetric density can be applied to logistic, double exponential and t-distributions as well as a normal distribution. The conditions can be also applied to scale mixtures of normal distributions. Finally, some similar results are developed in the scale family.
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Bibliographic InfoPaper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-296.
Length: 29 pages
Date of creation: Aug 2004
Date of revision:
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