Admissible and minimax multiparameter estimation in exponential families |
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Authors: | Malay Ghosh Ahmad Parsian |
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Affiliation: | Department of Statistics, Iowa State University, Ames, Iowa 50011 USA |
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Abstract: | Consider p independent distributions each belonging to the one parameter exponential family with distribution functions absolutely continuous with respect to Lebesgue measure. For estimating the natural parameter vector with p ≥ p0 (p0 is typically 2 or 3), a general class of estimators dominating the minimum variance unbiased estimator (MVUE) or an estimator which is a known constant multiple of the MVUE is produced under different weighted squared error losses. Included as special cases are some results of Hudson [13] and Berger [5]. Also, for a subfamily of the general exponential family, a class of estimators dominating the MVUE of the mean vector or an estimator which is a known constant multiple of the MVUE is produced. The major tool is to obtain a general solution to a basic differential inequality. |
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Keywords: | Admissibility minimaxity natural parameter vector mean vector squared norm loss weighted squared error loss normal gamma |
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