Title: On Being Bayes and Unbiasedness

Author(s): Siamak Noorbaloochi and Glen Meeden
Issue: Volume 80 Series A Part 1 Year 2018
Pages: 152 -- 167
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.
AMS (2000) subject classification. Primary: 62F10, 62F15; Secondary: 47A05, 46C07.
Keywords and phrases: Unbiasedness, Bayes estimators, Squared error loss, Consistency