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Teor. Veroyatnost. i Primenen., 1968, Volume 13, Issue 2, Pages 359–361 (Mi tvp857)  

Short Communications

A quadratic error of the estimation of multidimensional normal distribution densities

G. M. Maniya

Problem Research Laboratory of Applied Mathematics, Tbilisi State University

Abstract: It is proved that the distributions of the variables
$$ n\int_{R^N}[P(x)-P^*_n(x)]^2dx $$
(where $P(x)$ is the density of an $N$-dimensional normal distribution, $P^*(x)$ is the corresponding empirical density, i.e. a normal density with the mean and covariance matrix equalled the empirical mean and empirical covariance matrix respectively, constructed by the sample of size $n$, $R^N$ being the $N$-dimensional space of real vectors $x=(x_1,x_2,…,x_N)$) converge to the distribution of the sum of two independent quadratic forms.

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English version:
Theory of Probability and its Applications, 1968, 13:2, 341–343

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Received: 22.02.1967

Citation: G. M. Maniya, “A quadratic error of the estimation of multidimensional normal distribution densities”, Teor. Veroyatnost. i Primenen., 13:2 (1968), 359–361; Theory Probab. Appl., 13:2 (1968), 341–343

Citation in format AMSBIB
\Bibitem{Man68}
\by G.~M.~Maniya
\paper A~quadratic error of the estimation of multidimensional normal distribution densities
\jour Teor. Veroyatnost. i Primenen.
\yr 1968
\vol 13
\issue 2
\pages 359--361
\mathnet{http://mi.mathnet.ru/tvp857}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=246404}
\zmath{https://zbmath.org/?q=an:0167.47401|0162.50502}
\transl
\jour Theory Probab. Appl.
\yr 1968
\vol 13
\issue 2
\pages 341--343
\crossref{https://doi.org/10.1137/1113043}


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