Matematičeskie zametki, Tome 6 (1969) no. 1, pp. 81-89
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A. M. Kagan; O. V. Shalaevskii. Admissibility of the estimate of least squares. Unusual property of the normal law. Matematičeskie zametki, Tome 6 (1969) no. 1, pp. 81-89. http://geodesic.mathdoc.fr/item/MZM_1969_6_1_a9/
@article{MZM_1969_6_1_a9,
author = {A. M. Kagan and O. V. Shalaevskii},
title = {Admissibility of the estimate of least squares. {Unusual} property of the normal law},
journal = {Matemati\v{c}eskie zametki},
pages = {81--89},
year = {1969},
volume = {6},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1969_6_1_a9/}
}
TY - JOUR
AU - A. M. Kagan
AU - O. V. Shalaevskii
TI - Admissibility of the estimate of least squares. Unusual property of the normal law
JO - Matematičeskie zametki
PY - 1969
SP - 81
EP - 89
VL - 6
IS - 1
UR - http://geodesic.mathdoc.fr/item/MZM_1969_6_1_a9/
LA - ru
ID - MZM_1969_6_1_a9
ER -
%0 Journal Article
%A A. M. Kagan
%A O. V. Shalaevskii
%T Admissibility of the estimate of least squares. Unusual property of the normal law
%J Matematičeskie zametki
%D 1969
%P 81-89
%V 6
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_1969_6_1_a9/
%G ru
%F MZM_1969_6_1_a9
It is shown that in the linear-regression scheme, the estimates of the squares of parametric vector-functions are admissible in the class of unbiased estimates if and only if the observations obey a normal law. Here, the covariation matrix (non-negative definite) serves as a measure of the quality of the estimate.
