Abstract
The problem considered is simultaneous estimation of scale parameters and their reciprocals from p independent gamma distributions under a scale invariant loss function first introduced in James and Stein (1961). Under mild restrictions on the shape parameters, the best scale invariant estimators are shown to be admissible for p = 2. For p ≥ 3, a general technique is developed for improving upon the best scale invariant estimators. Improvement on the generalized Bayes estimators of a vector involving certain powers of the scale parameter is also obtained.
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