A new signed rank test based on slopes of vectors for bivariate location problems

The proposed test is based on the slopes obtained by using two vectors. The test statistic does not depend on the covariance structure of the population, and is scale-invariant and robust to outliers. The asymptotic relative efficiency of the proposed test statistic with respect to Hotelling's T ² indicates superior performance of the proposed test statistic under heavy-tailed distributions. A complete comparison of the proposed test with some of the existing test statistics is also provided. For non-normal distributions, a Monte Carlo simulation study shows that the proposed test statistic performs better than most of the existing test statistics compared here for almost all the shifts in the location. Application of the test is also illustrated using a real-life bivariate data set.