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Probl. Peredachi Inf., 1975, Volume 11, Issue 3, Pages 31–43 (Mi ppi1593)  

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

Methods of Signal Processing

Parameter Estimation for a Discontinuous Signal in White Gaussian Noise

I. A. Ibragimov, R. Z. Khas'minskii


Abstract: It is shown that for a discontinuous and quasidiscontinuous signal $S(t-\theta)$ the quadratic risk of the estimate of the parameter $\theta$ in white Gaussian noise of spectral density $\varepsilon^2$ is proportional to $\varepsilon^4$ when $\varepsilon\to 0$. The minimum attainable coefficient for $\varepsilon^4$ is found, as well as estimates for which this minimum is attained. It is shown that the maximum-likelihood estimate in this sense is inferior to the optimum one by roughly a factor of 1.3 when $\varepsilon\to 0$. The limiting distributions of the estimates are also found; they are non-Gaussian but general for all $S(t)$ with discontinuities of the first kind. The only parameter that appears in these distributions is the number $r^2$, this being equal to the sum of squares of the discontinuities of $S(t-\theta)$ in the observation interval.

Full text: PDF file (778 kB)

English version:
Problems of Information Transmission, 1975, 11:3, 203–212

Bibliographic databases:

UDC: 621.391.1:519.25
Received: 24.03.1974

Citation: I. A. Ibragimov, R. Z. Khas'minskii, “Parameter Estimation for a Discontinuous Signal in White Gaussian Noise”, Probl. Peredachi Inf., 11:3 (1975), 31–43; Problems Inform. Transmission, 11:3 (1975), 203–212

Citation in format AMSBIB
\Bibitem{IbrKha75}
\by I.~A.~Ibragimov, R.~Z.~Khas'minskii
\paper Parameter Estimation for a~Discontinuous Signal in White Gaussian Noise
\jour Probl. Peredachi Inf.
\yr 1975
\vol 11
\issue 3
\pages 31--43
\mathnet{http://mi.mathnet.ru/ppi1593}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=501542}
\zmath{https://zbmath.org/?q=an:0334.60019}
\transl
\jour Problems Inform. Transmission
\yr 1975
\vol 11
\issue 3
\pages 203--212


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Novikov, N. E. Kordzahiya, “Pitman estimators: an asymptotic variance revisited”, Theory Probab. Appl., 57:3 (2013), 521–529  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. G. K. Golubev, V. G. Potapov, “On statistical problems in geolocation”, Problems Inform. Transmission, 49:3 (2013), 249–275  mathnet  crossref  isi  elib
    3. A. A. Novikov, N. E. Kordzahiya, T. Ling, “On moments of Pitman estimators: the case of fractional Brownian motion”, Theory Probab. Appl., 58:4 (2014), 601–614  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • Проблемы передачи информации Problems of Information Transmission
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