On the $\varepsilon$-minimax character of the hotelling $T^2$ test for nonnormal distributions

L. A. Khalfin, N. M. Khalfina

V. A. Steklov Mathematics Institute, Leningrad Branch, Academy of Sciences, SSSR

Abstract: 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 $O(\varepsilon)$.

UDC: 512.2

Received: 26.06.1970

 English version: Mathematical Notes, 1972, 11:5, 322–327

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