A Nonparametric Test for the One-Sample Bivariate Location Problem

A nonparametric test is proposed for the bivariate one-sample location problem. The proposed test is robust in nature. The asymptotic distribution of the test statistic is computed as Chi-square. The power of the proposed test statistic is compared with Hotelling's T² test statistic, Mardia's (1967) test statistic, Blumen's (1958) test statistic, and Wilcoxon's rank sum test statistic using Monte Carlo techniques. The proposed test statistic performs better than its competitors considered here under almost all the underlying distributions used for the power study. The application of the test is illustrated using a bivariate one sample data.