It is shown in infinite-dimensional Gaussian problems that affine estimators minimax the variance among all estimators of a linear functional subject to a constraint on the bias. Likewise, affine estimators also minimax the square of the bias among all estimates of a linear functional subject to a constraint on the variance.
Publié le : 1995-06-14
Classification:
Bias-variance tradeoff,
Cramer-Rao inequality,
minimax risk,
white noise model,
modulus of continuity,
62C05,
62E20,
62J02,
62G05,
62M99
@article{1176324624,
author = {Low, Mark G.},
title = {Bias-Variance Tradeoffs in Functional Estimation Problems},
journal = {Ann. Statist.},
volume = {23},
number = {6},
year = {1995},
pages = { 824-835},
language = {en},
url = {http://dml.mathdoc.fr/item/1176324624}
}
Low, Mark G. Bias-Variance Tradeoffs in Functional Estimation Problems. Ann. Statist., Tome 23 (1995) no. 6, pp. 824-835. http://gdmltest.u-ga.fr/item/1176324624/