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Teor. Veroyatnost. i Primenen., 1980, Volume 25, Issue 4, Pages 718–733 (Mi tvp1227)  

This article is cited in 3 scientific papers (total in 3 papers)

On the estimates of the signal, its derivatives and the point of maximum for Gaussian observations

I. A. Ibragimova, R. Z. Has'minskiĭb

a Leningrad
b Moscow

Abstract: 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.

Full text: PDF file (909 kB)

English version:
Theory of Probability and its Applications, 1981, 25:4, 703–720

Bibliographic databases:

Received: 24.09.1979

Citation: I. A. Ibragimov, R. Z. Has'minskiǐ, “On the estimates of the signal, its derivatives and the point of maximum for Gaussian observations”, Teor. Veroyatnost. i Primenen., 25:4 (1980), 718–733; Theory Probab. Appl., 25:4 (1981), 703–720

Citation in format AMSBIB
\Bibitem{IbrKha80}
\by I.~A.~Ibragimov, R.~Z.~Has'minski{\v\i}
\paper On the estimates of the signal, its derivatives and the point of maximum for Gaussian observations
\jour Teor. Veroyatnost. i Primenen.
\yr 1980
\vol 25
\issue 4
\pages 718--733
\mathnet{http://mi.mathnet.ru/tvp1227}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=595134}
\zmath{https://zbmath.org/?q=an:0471.60050|0454.60042}
\transl
\jour Theory Probab. Appl.
\yr 1981
\vol 25
\issue 4
\pages 703--720
\crossref{https://doi.org/10.1137/1125086}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980MK50200004}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. P.-L. Chow, R. Z. Khas'minskii, “On-line Estimation of Smooth Signals with Partial Observation”, Problems Inform. Transmission, 42:4 (2006), 330–339  mathnet  crossref  mathscinet
    2. R. Z. Khasminskii, “Nonparametric Estimation of Signal Amplitude in White Gaussian Noise”, Problems Inform. Transmission, 44:4 (2008), 315–320  mathnet  crossref  mathscinet  zmath  isi
    3. I. A. Ibragimov, “A generalization of Chentsov's projection estimates”, J. Math. Sci. (N. Y.), 204:1 (2015), 116–133  mathnet  crossref  mathscinet
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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