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.
Publié le : 1994-03-14
Classification:
Bounded normal mean,
estimation of linear functionals,
confidence statements for linear functionals,
modulus of continuity,
minimax risk,
nonparametric regression,
density estimation,
62C20,
62G07,
41A25,
43A30
@article{1176325367,
author = {Donoho, David L.},
title = {Statistical Estimation and Optimal Recovery},
journal = {Ann. Statist.},
volume = {22},
number = {1},
year = {1994},
pages = { 238-270},
language = {en},
url = {http://dml.mathdoc.fr/item/1176325367}
}
Donoho, David L. Statistical Estimation and Optimal Recovery. Ann. Statist., Tome 22 (1994) no. 1, pp. 238-270. http://gdmltest.u-ga.fr/item/1176325367/