Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 4, pp. 718-733
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I. A. Ibragimov; R. Z. Has'minskiǐ. On the estimates of the signal, its derivatives and the point of maximum for Gaussian observations. Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 4, pp. 718-733. http://geodesic.mathdoc.fr/item/TVP_1980_25_4_a3/
@article{TVP_1980_25_4_a3,
author = {I. A. Ibragimov and R. Z. Has'minskiǐ},
title = {On the estimates of the signal, its derivatives and the point of maximum for {Gaussian} observations},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {718--733},
year = {1980},
volume = {25},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1980_25_4_a3/}
}
TY - JOUR
AU - I. A. Ibragimov
AU - R. Z. Has'minskiǐ
TI - On the estimates of the signal, its derivatives and the point of maximum for Gaussian observations
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1980
SP - 718
EP - 733
VL - 25
IS - 4
UR - http://geodesic.mathdoc.fr/item/TVP_1980_25_4_a3/
LA - ru
ID - TVP_1980_25_4_a3
ER -
%0 Journal Article
%A I. A. Ibragimov
%A R. Z. Has'minskiǐ
%T On the estimates of the signal, its derivatives and the point of maximum for Gaussian observations
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1980
%P 718-733
%V 25
%N 4
%U http://geodesic.mathdoc.fr/item/TVP_1980_25_4_a3/
%G ru
%F TVP_1980_25_4_a3
We propose the estimates of the «signal» $S(t)$ and of its derivatives for the case when the observed process $X_\varepsilon(t)$ has the form (0.1). These estimates have asymptotically optimal rate of convergence to the unknown value of the «parameter» for a wide class of a priori assumptions on $S$ and on the loss functions. The analogous results for the estimates of the point of maximum of $S(t)$ are obtained also.
