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Teor. Veroyatnost. i Primenen., 1967, Volume 12, Issue 3, Pages 418–425 (Mi tvp724)  

An asymptotic expansion for the distribution of the maximum likelihood estimation of a vektor parameter

N. M. Mitrofanova

Leningrad

Abstract: Let $X$ he a random variable with a distribution function $f(x,\theta)$ depending on a vector parameter $\theta=(\theta,…,\theta_r)$. Let $\widehat\theta_n$ be the maximum likelihood estimate of $\theta$ corresponding to a sample of size $n$. It is proved that under certain conditions on $f(x,\theta)$ the distribution function of $\widehat\theta_n$ has an asymptotic expansion on $n^{1/2}$ with the number of terms depending on properties of $f(x,\theta)$.

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English version:
Theory of Probability and its Applications, 1967, 12:3, 364–372

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Received: 05.07.1966

Citation: N. M. Mitrofanova, “An asymptotic expansion for the distribution of the maximum likelihood estimation of a vektor parameter”, Teor. Veroyatnost. i Primenen., 12:3 (1967), 418–425; Theory Probab. Appl., 12:3 (1967), 364–372

Citation in format AMSBIB
\Bibitem{Mit67}
\by N.~M.~Mitrofanova
\paper An asymptotic expansion for the distribution of the maximum likelihood estimation of a~vektor parameter
\jour Teor. Veroyatnost. i Primenen.
\yr 1967
\vol 12
\issue 3
\pages 418--425
\mathnet{http://mi.mathnet.ru/tvp724}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=219162}
\zmath{https://zbmath.org/?q=an:0159.47803}
\transl
\jour Theory Probab. Appl.
\yr 1967
\vol 12
\issue 3
\pages 364--372
\crossref{https://doi.org/10.1137/1112048}


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