Abstract
New formulas are given for the minimax linear risk in estimating a linear functional of an unknown object from indirect data contaminated with random Gaussian noise. The formulas cover a variety of loss functions and do not require the symmetry of the convex a priori class. It is shown that affine minimax rules are within a few percent of minimax even among nonlinear rules, for a variety of loss functions. It is also shown that difficulty of estimation is measured by the modulus of continuity of the functional to be estimated. The method of proof exposes a correspondence between minimax affine estimates in the statistical estimation problem and optimal algorithms in the theory of optimal recovery.
Citation
David L. Donoho. "Statistical Estimation and Optimal Recovery." Ann. Statist. 22 (1) 238 - 270, March, 1994. https://doi.org/10.1214/aos/1176325367
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