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MR1397511 62H10 (62E20)
Kano, Yutaka An asymptotic expansion of the distribution of Hotelling's $T^2$-statistic under general distributions. MSI-2000, Vol. I (Honolulu, HI, 1995). Amer. J. Math. Management Sci. 15 (1995), no. 3-4, 317–341.
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