Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 2, pp. 388-395
Citer cet article
B. S. Cirel'son. Geometrical approach to the maximum likelihood estimation for infinite-dimensional Gaussian location. I. Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 2, pp. 388-395. http://geodesic.mathdoc.fr/item/TVP_1982_27_2_a24/
@article{TVP_1982_27_2_a24,
author = {B. S. Cirel'son},
title = {Geometrical approach to the maximum likelihood estimation for infinite-dimensional {Gaussian} {location.~I}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {388--395},
year = {1982},
volume = {27},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1982_27_2_a24/}
}
TY - JOUR
AU - B. S. Cirel'son
TI - Geometrical approach to the maximum likelihood estimation for infinite-dimensional Gaussian location. I
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1982
SP - 388
EP - 395
VL - 27
IS - 2
UR - http://geodesic.mathdoc.fr/item/TVP_1982_27_2_a24/
LA - ru
ID - TVP_1982_27_2_a24
ER -
%0 Journal Article
%A B. S. Cirel'son
%T Geometrical approach to the maximum likelihood estimation for infinite-dimensional Gaussian location. I
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1982
%P 388-395
%V 27
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_1982_27_2_a24/
%G ru
%F TVP_1982_27_2_a24
The MLE for the mean of the infinite-dimensional Gaussian measure with given covariance is studied; we assume that the mean belongs to a given set $V$ and relate the behaviour of MLE with the metric properties of $V$ (the metric is induced by the covariance). For example, a Hölder signal in the white noise admits the MLE if the Hölder exponent is greater than $1/2$ . Some inequalities for the distance between the mean and its MLE are given.
