A bivariate signed rank test for two sample location problem

An affine-invariant signed rank test for the difference in location between two symmetric populations is proposed. The proposed test statistic is compared with Hotelling's T-2 statistic, Mardia's(1967)test statistic, Peters-Randles(1991) test statistic and Wilcoxon's rank sum test statistic using a Monte Carlo Study. It performs better than Mardia's test statistic under almost all populations considered. Under the bivariate normal distribution, it performs better than other test statistics compared for small differences in location between two populations except Hotelling's T-2. It performs better than all statistics, including Hotelling's T-2, for sample size 15 when samples are drawn from Pearson type II. Pearson type VII, bivariate normal mixtures and populations 6 and 7 for small differences in location between the two populations, For heavy tailed population 6, the proposed test statistic performs as good as Hotelling's T-2 and Wilcoxon's test statistic for sample size 25, A Huber type Robust version ( see for example, Huber(1977)) of the proposed test statistic is also found useful.