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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 441, Pages 187–203 (Mi znsl6233)  
On a problem of estimation of an infinite-dimensional parameter

V. A. Ershova, I. A. Ibragimovab

a St. Petersburg State University, St. Petersburg, Russia
b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
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Abstract: Let $X$ be a random variable taking the positive integer values and let $\mathbf P\{X=k\}=\theta(k)$. We consider the problem of estimation of the parameter $\theta=(\theta(1),\theta(2),\dots)$ on the base of the sample $X_1,X_2,\dots,X_n$ where the observations $X_j$ are independent copies of $X$.
Key words and phrases: non-parametric estimates, maximum likelihood estimation.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00856
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Received: 18.11.2015
English version:
Journal of Mathematical Sciences (New York), 2016, Volume 219, Issue 5, Pages 731–742
DOI: https://doi.org/10.1007/s10958-016-3142-1
Bibliographic databases:
Document Type: Article
UDC: 519
Language: Russian
Citation: V. A. Ershov, I. A. Ibragimov, “On a problem of estimation of an infinite-dimensional parameter”, Probability and statistics. Part 22, Zap. Nauchn. Sem. POMI, 441, POMI, St. Petersburg, 2015, 187–203; J. Math. Sci. (N. Y.), 219:5 (2016), 731–742
Citation in format AMSBIB
\Bibitem{ErsIbr15}
\by V.~A.~Ershov, I.~A.~Ibragimov
\paper On a~problem of estimation of an infinite-dimensional parameter
\inbook Probability and statistics. Part~22
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 441
\pages 187--203
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6233}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3504505}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 219
\issue 5
\pages 731--742
\crossref{https://doi.org/10.1007/s10958-016-3142-1}
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