Admissible and minimax multiparameter estimation in exponential families

Malay Ghosh and Ahmad Parsian

Journal of Multivariate Analysis, 1980, vol. 10, issue 4, 551-564

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.

Keywords: Admissibility; minimaxity; natural; parameter; vector; mean; vector; squared; norm; loss; weighted; squared; error; loss; normal; gamma (search for similar items in EconPapers)
Date: 1980
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