CIRJE-F-270 | "Minimaxity in Estimation of Restricted Parameters" |
Author Name | Kubokawa, Tatsuya |
Date | March 2004 |
Full Paper | PDF file@ |
Remarks | Subsequently published in Journal of the Japan Statistical Society, (2004), 34, 229-253, vol.34; revised in May 2004. |
Abstract |
This 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. |