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Zapiski Nauchnykh Seminarov POMI, 2013, Volume 412, Pages 181–206 (Mi znsl5648)  
A generalization of Chentsov's projection estimates

I. A. Ibragimovab

a St. Petersburg Department of Steklov Mathematical Institute, St. Petersburg, Russia
b St. Petersburg State University, St. Petersburg, Russia
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Abstract: In 1962, N. N. Chentsov suggested the following method of estimation a functional parameter $\theta$ belonging to a Hilbert space $H$. He suggested to project $\theta$ on finite-dimensional subspaces of $H$ and consider as estimates of $\theta$ estimates of these projections. In this paper, we suggest to consider the projections on all reproducing kernel subspaces of $H$.
Key words and phrases: Chentsov's projection estimates, non-parametric estimation theory, kernel estimates, reproducing kernels.
Received: 23.04.2013
English version:
Journal of Mathematical Sciences (New York), 2015, Volume 204, Issue 1, Pages 116–133
DOI: https://doi.org/10.1007/s10958-014-2190-7
Bibliographic databases:
Document Type: Article
UDC: 519.2
Language: Russian
Citation: I. A. Ibragimov, “A generalization of Chentsov's projection estimates”, Probability and statistics. Part 19, Zap. Nauchn. Sem. POMI, 412, POMI, St. Petersburg, 2013, 181–206; J. Math. Sci. (N. Y.), 204:1 (2015), 116–133
Citation in format AMSBIB
\Bibitem{Ibr13}
\by I.~A.~Ibragimov
\paper A generalization of Chentsov's projection estimates
\inbook Probability and statistics. Part~19
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 412
\pages 181--206
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5648}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3073543}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 204
\issue 1
\pages 116--133
\crossref{https://doi.org/10.1007/s10958-014-2190-7}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84925465069}
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