Minimaxity in Estimation of Restricted Parameters
AbstractThis paper is concerned with estimation of the restricted parameters in location and/or scale families from a decision-theoretic point of view. A simple method is provided to show the minimaxity of the best equivariant and unrestricted estimators. This is based on a modification of the known method of Girshick and Savage (1951) and can be applied to more complicated cases of restriction in the location-scale family. Classes of minimax estimators are also constructed by using the IERD method of Kubokawa (1994a, b): Especially, the paper succeeds in constructing such a class for estimating a restricted mean in a normal distribution with an unknown variance.
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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-270.
Length: 24 pages
Date of creation: Mar 2004
Date of revision:
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- Kubokawa, Tatsuya & Strawderman, William E., 2011. "A unified approach to non-minimaxity of sets of linear combinations of restricted location estimators," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1429-1444, November.
- Tatsuya Kubokawa & �ric Marchand & William E. Strawderman & Jean-Philippe Turcotte, 2012. "Minimaxity in Predictive Density Estimation with Parametric Constraints," CIRJE F-Series CIRJE-F-843, CIRJE, Faculty of Economics, University of Tokyo.
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