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On uniformly minimum variance unbiased estimation when no complete sufficient statistics exist


A simple generalization of the Lehmann-Scheffé theorem is given. It is used to find cases when UMVUE's exist but complete sufficient statistics do not. Another method to find such cases is also presented.

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Bondesson, L. On uniformly minimum variance unbiased estimation when no complete sufficient statistics exist. Metrika 30, 49–54 (1983).

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  • Unbiased Estimator
  • Simple Generalization
  • Random Mechanism
  • Convex Loss Function
  • Minimal Sufficient Statistic