Abstract:
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 $K_T(t, s)$, $K_T(t,t)\le T$.
Key words and phrases:
nonparametric estimation problems, estimation of functions, reproducing kernel spaces.
Citation:
I. A. Ibragimov, “On estimation of functions of a parameter observed in Gaussian noise”, Probability and statistics. Part 25, Zap. Nauchn. Sem. POMI, 457, POMI, St. Petersburg, 2017, 183–193; J. Math. Sci. (N. Y.), 238:4 (2019), 463–470
\Bibitem{Ibr17}
\by I.~A.~Ibragimov
\paper On estimation of functions of a~parameter observed in Gaussian noise
\inbook Probability and statistics. Part~25
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 457
\pages 183--193
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6442}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2019
\vol 238
\issue 4
\pages 463--470
\crossref{https://doi.org/10.1007/s10958-019-04250-9}
Linking options:
https://www.mathnet.ru/eng/znsl6442
https://www.mathnet.ru/eng/znsl/v457/p183
This publication is cited in the following 1 articles:
A. A. Borovkov, Al. V. Bulinski, A. M. Vershik, D. Zaporozhets, A. S. Holevo, A. N. Shiryaev, “Ildar Abdullovich Ibragimov (on his ninetieth birthday)”, Russian Math. Surveys, 78:3 (2023), 573–583
Citation in format AMSBIB
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