Abstract
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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Acknowledgments
Research was supported in part by IIR 12-340 –HSR&D grant, Department of Veterans Affairs, Veterans Health Administration, Office of Research and Development.
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Noorbaloochi, S., Meeden, G. On Being Bayes and Unbiasedness. Sankhya A 80, 152–167 (2018). https://doi.org/10.1007/s13171-017-0097-3
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DOI: https://doi.org/10.1007/s13171-017-0097-3