Title: The multivariate rank tests based on the likelihood ratio
Authors: Soshi Kawada - Tokyo University of Science (Japan) [presenting]
Hidetoshi Murakami - Tokyo University of Science (Japan)
Abstract: Testing hypothesis is one of the most important topics in nonparametric statistics. Various nonparametric tests have been proposed for two-sample and multisample testing problems involving location, scale and location-scale parameters. It is well known that the nonparametric rank statistics based on the likelihood ratio is powerful and robust statistics. Recent progress in computerized measurement technology has permitted the accumulation of multivariate data, increasing the importance of multivariate data in many scientific fields. Thus, a multivariate examination of the data is very appropriate. However, in many applications, the underlying distribution cannot be assumed to follow a specific distribution, and nonparametric hypothesis testing must be used. For multivariate data, it is important to determine how to represent rank based on observation distances. We apply the extended Jureckova-Kalinas rank of distance to the rank statistics based on the likelihood ratio. Jureckova-Kalina rank of distance is invariant under affine transformation with respect to the shifted location. We compare the powers of the proposed test with the multivariate two-sample and multisample nonparametric tests for various distributions by using simulation studies.