Suppose that the null distribution function of some test statistic S = Sn is expanded in terms of χ2 distributions. In this paper we provide a method for finding a ‘monotone’ transformation T(x) such that T(S) has chi-squared distribution to order n−k. This technique is applied to the special case of Hotelling's T2-statistic.
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Yoshihide Kakizawa (1996) studied this question.
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