A BIVARIATE SIGNED RANK TEST FOR THE 2-SAMPLE LOCATION PROBLEM

A signed rank affine invariant test for the difference in location between two elliptically symmetric populations is proposed. Asymptotic properties of the test are developed under the null hypothesis and under contiguous alternatives. The proposed statistic is compared with three of its competitors using Monte Carlo studies and Pitman asymptotic relative efficiencies. It is seen that the signed rank statistic introduced is especially powerful when the underlying distribution is light tailed. For heavy-tailed distributions a bivariate test due to Mardia is preferred. However, the proposed statistic performs better than Hotelling's T2-statistic for both light- and heavy-tailed populations, performing almost as well as Hotelling's T2-statistic under bivariate normality.