A new method to determine separated hyper-plane for non-parametric sign test in multivariate data (original) (raw)

Non-parametric testing is very necessary in case that the statistical sample does not conform normal distribution or we have no knowledge about sample distribution. Sign test is a popular and effective test for non-parametric model but it cannot be applied into multivariate data in which observations are vectors because the ordering and comparative operators are not defined in n-dimension vector space. So, this research proposes a new approach to perform sign test on multivariate sample by using a hyper-plane to separate multi-dimensional observations into two sides. Therefore, it is possible for the sign test to assign plus signs and minus signs to observations in each side. Moreover, this research introduces a new method to determine the separated hyper-plane. This method is a variant of support vector machine (SVM), thus, the optimized hyper-plane is the one that contains null hypothesis and splits observations as discriminatively as possible.