Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 1, pp. 151-155
Citer cet article
G. M. Maniya. The squared error of the estimate of a multidimensional normal density function by the sample data. Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 1, pp. 151-155. http://geodesic.mathdoc.fr/item/TVP_1969_14_1_a17/
@article{TVP_1969_14_1_a17,
author = {G. M. Maniya},
title = {The squared error of the estimate of a~multidimensional normal density function by the sample data},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {151--155},
year = {1969},
volume = {14},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1969_14_1_a17/}
}
TY - JOUR
AU - G. M. Maniya
TI - The squared error of the estimate of a multidimensional normal density function by the sample data
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1969
SP - 151
EP - 155
VL - 14
IS - 1
UR - http://geodesic.mathdoc.fr/item/TVP_1969_14_1_a17/
LA - ru
ID - TVP_1969_14_1_a17
ER -
%0 Journal Article
%A G. M. Maniya
%T The squared error of the estimate of a multidimensional normal density function by the sample data
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1969
%P 151-155
%V 14
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_1969_14_1_a17/
%G ru
%F TVP_1969_14_1_a17
It has been proved in [2] that the distributions of the variables $$ n\int_{R^k}[p(x)-p^*_n(x)]^2\,dx $$ converge as $n\to\infty$ to the distribution of the sum of two independent quadratic forms. In the paper the distributions of these quadratic forms are obtained.
