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Admissible and minimax multiparameter estimation in exponential families

Author

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  • Ghosh, Malay
  • Parsian, Ahmad

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.

Suggested Citation

  • Ghosh, Malay & Parsian, Ahmad, 1980. "Admissible and minimax multiparameter estimation in exponential families," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 551-564, December.
    • Handle: RePEc:eee:jmvana:v:10:y:1980:i:4:p:551-564
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