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

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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},
     publisher = {mathdoc},
     volume = {457},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_457_a9/}
}
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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/