On the power of sen-mathur test statistic

Sen-Mathur [10] paper deals with the bivariate location problem. Sen-Mathur [10] proved that the proposed test statistic performs better than some of the existing methods using simulation studies but no power function and asymptotic results were provided. In this paper we present the power function and asymptotic behavior of a consistent test for difference in locations between two bivariate populations proposed by Sen-Mathur [10]. The power function is evaluated under two distributions. With the power function, we find that Sen-Mathur [10] test is more powerful than Wilcoxon bivariate rank sum test for location for moderate and large difference in locations. The S-Plus code is provided to evaluate the power function.