Abstract
An affine-invariant signed sum test based on interdirections is proposed for the one-sample multivariate location problem. The test proposed, including the two-sided univariate Wilcoxon signed-rank test as a special case, is somewhat like applying the interdirection sign test to the sums of pairs of observed vectors. The proposed statistic is shown to have a limiting x 2 p null distribution when the underlying distribution is elliptically symmetric. In addition, the asymptotic distribution of the statistic under certain contiguous alternatives is obtained for elliptically symmetric distributions with a particular density function form. Comparisons made between the proposed test and Hotelling's T 2 via Pitman asymptotic relative efficiencies show the signed sum test performs better than Hotelling's T 2 when the underlying distribution is heavy-tailed.
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