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Teoriya Veroyatnostei i ee Primeneniya, 1974, Volume 19, Issue 2, Pages 245–255 (Mi tvp2826)  

This article is cited in 9 scientific papers (total in 9 papers)

On sequential estimation

I. A. Ibragimova, R. Z. Khas'minskiib

a Leningrad
b Moscow
Full-text PDF (591 kB) Citations (9)
Abstract: The main result of this paper is
Theorem 1. {\em Let $X_1,\dots,X_n$ be independent observations with probability density $f(x,\theta)$, $\theta\in\Theta\subset R^1$. Let the following conditions be satisfied:
1) $f(x,\theta)$ is absolutely continuous as a function of $\theta$ in some neighbourhood of $\theta=t$ for all $x$;
2) for each $\theta$, derivative $\partial f(x,\theta)/\partial\theta$ exists in some neighbourhood of $t$ for $\nu$-almost all $x$;
3) the function $I(\theta)$ (see (1.1)) is continuous at $\theta=t$.
Let $(\{T_m^{(n)}\},\tau_n)$ be a sequential estimation procedure and $E_\theta\tau_n=n$. Then, for any $a>0$, inequality (1.3) holds true.}
This theorem shows that for the loss function $|x|^a$ sequential estimation does not give advantage in the asymptotically minimax sense.
Received: 04.05.1973
English version:
Theory of Probability and its Applications, 1975, Volume 19, Issue 2, Pages 233–244
DOI: https://doi.org/10.1137/1119031
Bibliographic databases:
Language: Russian
Citation: I. A. Ibragimov, R. Z. Khas'minskii, “On sequential estimation”, Teor. Veroyatnost. i Primenen., 19:2 (1974), 245–255; Theory Probab. Appl., 19:2 (1975), 233–244
Citation in format AMSBIB
\Bibitem{IbrKha74}
\by I.~A.~Ibragimov, R.~Z.~Khas'minskii
\paper On sequential estimation
\jour Teor. Veroyatnost. i Primenen.
\yr 1974
\vol 19
\issue 2
\pages 245--255
\mathnet{http://mi.mathnet.ru/tvp2826}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=343504}
\zmath{https://zbmath.org/?q=an:0316.62031}
\transl
\jour Theory Probab. Appl.
\yr 1975
\vol 19
\issue 2
\pages 233--244
\crossref{https://doi.org/10.1137/1119031}
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  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теория вероятностей и ее применения Theory of Probability and its Applications
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