A multivariate signed-rank test for the one-sample location problem.

*(English)*Zbl 0709.62051Summary: An affine-invariant signed-rank test is proposed for the one-sample multivariate location problem. The test suggested is a modification of Randles’s multivariate sign test [the second author, ibid. 84, No. 408, 1045–1050 (1989; Zbl 0702.62039)] based on interdirections, which extends Blumen’s bivariate procedure [I. Blumen, ibid 53, 448–456 (1958; Zbl 0087.14702)] to the multidimensional setting. Comparisons are made between the proposed statistic and several competitors via Pitman asymptotic relative efficiencies and Monte Carlo results. The signed-rank statistic appears to be robust. It performs better than its competitors when the distribution is light-tailed, and virtually as well as Hotelling’s \(T^ 2\) under multivariate normality. For heavy-tailed distributions the signed-rank statistic performs better than Hotelling’s \(T^ 2\) but not as well as Randles’s statistic.

##### MSC:

62H15 | Hypothesis testing in multivariate analysis |