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). https://doi.org/10.1007/BF02056900
- Unbiased Estimator
- Simple Generalization
- Random Mechanism
- Convex Loss Function
- Minimal Sufficient Statistic