Geodesic
On estimation of functions of a parameter observed in Gaussian noise
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 25, Tome 457 (2017), pp. 183-193 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The main problem of the paper looks as follows. A functional parameter $\theta\in\Theta\subset L_2(-\infty,\infty)$ is observed in Gaussian noise. The problem is to estimate the value $F(\theta)$ of a given function $F$. A construction of asymptotically efficient estimates for $F(\theta)$ is suggested under the conditions that $\Theta$ admits approximations by subspaces $H_T\subset L_2$ with the reproducing kernels $K_T(t, s)$, $K_T(t,t)\le T$. 
@article{ZNSL_2017_457_a9,
     author = {I. A. Ibragimov},
     title = {On estimation of functions of a~parameter observed in {Gaussian} noise},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {183--193},
     year = {2017},
     volume = {457},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_457_a9/}
}
TY  - JOUR
AU  - I. A. Ibragimov
TI  - On estimation of functions of a parameter observed in Gaussian noise
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2017
SP  - 183
EP  - 193
VL  - 457
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2017_457_a9/
LA  - ru
ID  - ZNSL_2017_457_a9
ER  - 
%0 Journal Article
%A I. A. Ibragimov
%T On estimation of functions of a parameter observed in Gaussian noise
%J Zapiski Nauchnykh Seminarov POMI
%D 2017
%P 183-193
%V 457
%U http://geodesic.mathdoc.fr/item/ZNSL_2017_457_a9/
%G ru
%F ZNSL_2017_457_a9
I. A. Ibragimov. On estimation of functions of a parameter observed in Gaussian noise. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 25, Tome 457 (2017), pp. 183-193. http://geodesic.mathdoc.fr/item/ZNSL_2017_457_a9/

[1] N. Aronszajn, “Theory of reproducing kernels”, Trans. Amer. Math. Soc., 68 (1950), 337–404 | DOI | MR | Zbl

[2] N. I. Akhiezer, Lektsii po teorii approksimatsii, Nauka, M., 1965 | MR

[3] P. Bickel, C. Klaassen, Y. Ritov, J. Wellner, Efficient and Adaptive Estimation for Semiparametric Models, J. Hopkins Univ. Press, 1993 | MR | Zbl

[4] I. A. Ibragimov, R. Z. Khasminskii, “Odna zadacha statisticheskogo otsenivaniya v gaussovskom belom shume”, Doklady AN SSSR, 326:6 (1977), 1300–1302 | MR

[5] I. A. Ibragimov, R. Z. Khasminskii, Asimptoticheskaya teoriya otsenivaniya, Nauka, M., 1979 | MR

[6] I. A. Ibragimov, R. Z. Khasminskii, “Ob otsenke plotnosti raspredeleniya prinadlezhaschei odnomu klassu tselykh funktsii”, Teor. veroyatn. i ee primen., 27:3 (1982), 514–524 | MR | Zbl

[7] I. A. Ibragimov, A. S. Nemirovskii, R. Z. Khasminskii, “Nekotorye zadachi neparametricheskogo otsenivaniya v gaussovskom belom shume”, Teor. veroyatn. i ee primen., 31:3 (1986), 451–466 | MR | Zbl

[8] K. Iosida, Funktsionalnyi analiz, Mir, M., 1967 | MR

[9] A. Nemirovski, Topics in Non-parametric Statistics, Lecture Notes in Mathematics, 1738, Springer, 2000 | MR | Zbl

[10] V. M. Tikhomirov, “Poperechniki mnozhestv v funktsionalnykh prostranstvakh i teoriya nailuchshikh priblizhenii”, Uspekhi mat. nauk, 20:3 (1960), 81–120 | MR | Zbl