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On Being Bayes and Unbiasedness

Noorbaloochi S, Meeden G. On Being Bayes and Unbiasedness. Sankhya A: The Indian Journal of Statistics. 2017 May 18; 79:1-16.

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Assuming squared error loss, we show that finding unbiased estimators and Bayes estimators can be treated as using a pair of linear operators that operate between two Hilbert spaces. We note that these integral operators are adjoint and then investigate some consequences of this fact. An extension to loss functions that can be defined via an inner product is also presented.

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