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March, 1994 Statistical Estimation and Optimal Recovery
David L. Donoho
Ann. Statist. 22(1): 238-270 (March, 1994). DOI: 10.1214/aos/1176325367


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.


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David L. Donoho. "Statistical Estimation and Optimal Recovery." Ann. Statist. 22 (1) 238 - 270, March, 1994.


Published: March, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0805.62014
MathSciNet: MR1272082
Digital Object Identifier: 10.1214/aos/1176325367

Primary: 62C20
Secondary: 41A25, 43A30, 62G07

Rights: Copyright © 1994 Institute of Mathematical Statistics


Vol.22 • No. 1 • March, 1994
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