Asymptotic null and nonnull distribution of Hotelling's T2-statistic under the elliptical distribution

This paper is concerned with asymptotic distribution of Hotelling's T²-statistic under the elliptical distribution for the null hypothesis and the local alternative under the elliptical distribution. Asymptotic expansions for the distribution of T² for the null case and the local alternative are given up to the order N⁻¹, where N is the sample size. The percentiles of T² and the approximate powers are calculated to evaluate the effect of the elliptical distribution for some numerical examples.Also to evaluate the effect of an adjustment of Bartlett type to Hotelling's T² for the local alternative, the approximate power of adjusted T² is calculated in comparison with one of nonadjusted T².