The asymptotic risk of efficient estimators with
Kullback–Leibler loss in smoothly parametrized statistical models is
$k/2_n$, where $k$ is the parameter dimension and $n$ is the sample
size. Under fairly general conditions, we given a simple information-theoretic
proof that the set of parameter values where any arbitrary estimator is
superefficient is negligible. The proof is based on a result of Rissanen that
codes have asymptotic redundancy not smaller than $(k/2)\log n$, except in a
set of measure 0.
Publié le : 1998-10-14
Classification:
Superefficiency,
information theory,
data compression,
Kullback–Leibler loss,
62F12,
94A65,
94A29,
62G20
@article{1024691358,
author = {Barron, Andrew and Hengartner, Nicolas},
title = {Information theory and superefficiency},
journal = {Ann. Statist.},
volume = {26},
number = {3},
year = {1998},
pages = { 1800-1825},
language = {en},
url = {http://dml.mathdoc.fr/item/1024691358}
}
Barron, Andrew; Hengartner, Nicolas. Information theory and superefficiency. Ann. Statist., Tome 26 (1998) no. 3, pp. 1800-1825. http://gdmltest.u-ga.fr/item/1024691358/