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
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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.
@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},
publisher = {mathdoc},
volume = {25},
number = {4},
year = {1980},
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 PB - mathdoc 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 %I mathdoc %U http://geodesic.mathdoc.fr/item/TVP_1980_25_4_a3/ %G ru %F TVP_1980_25_4_a3
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/