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.
Keywords
MinimaxMathematicsAffine transformationMathematical optimizationApplied mathematicsVariety (cybernetics)Minimax estimatorA priori and a posterioriStatisticsPure mathematicsEstimatorMinimum-variance unbiased estimator
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Publication Info
- Year
- 1994
- Type
- article
- Volume
- 22
- Issue
- 1
- Citations
- 267
- Access
- Closed
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Cite This
David L. Donoho
(1994).
Statistical Estimation and Optimal Recovery.
The Annals of Statistics
, 22
(1)
.
https://doi.org/10.1214/aos/1176325367
Identifiers
- DOI
- 10.1214/aos/1176325367