Geodesic
On the $\varepsilon$-minimax character of the hotelling $T^2$ test for nonnormal distributions
Matematičeskie zametki, Tome 11 (1972) no. 5, pp. 527-536 
L. A. Khalfin; N. M. Khalfina. On the $\varepsilon$-minimax character of the hotelling $T^2$ test for nonnormal distributions. Matematičeskie zametki, Tome 11 (1972) no. 5, pp. 527-536. http://geodesic.mathdoc.fr/item/MZM_1972_11_5_a6/
@article{MZM_1972_11_5_a6,
     author = {L. A. Khalfin and N. M. Khalfina},
     title = {On the $\varepsilon$-minimax character of the hotelling $T^2$ test for nonnormal distributions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {527--536},
     year = {1972},
     volume = {11},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_11_5_a6/}
}
TY  - JOUR
AU  - L. A. Khalfin
AU  - N. M. Khalfina
TI  - On the $\varepsilon$-minimax character of the hotelling $T^2$ test for nonnormal distributions
JO  - Matematičeskie zametki
PY  - 1972
SP  - 527
EP  - 536
VL  - 11
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MZM_1972_11_5_a6/
LA  - ru
ID  - MZM_1972_11_5_a6
ER  - 
%0 Journal Article
%A L. A. Khalfin
%A N. M. Khalfina
%T On the $\varepsilon$-minimax character of the hotelling $T^2$ test for nonnormal distributions
%J Matematičeskie zametki
%D 1972
%P 527-536
%V 11
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_1972_11_5_a6/
%G ru
%F MZM_1972_11_5_a6

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper investigates the robustness of the minimax property of the Hotelling test for distributions close to normal. It is proven that the $T^2$ test maximizes, among all tests, the level $\alpha$ of minimal power on the set of alternatives to within $O(\varepsilon)$.