Multivariate equivalence and component-wise superiority tests for paired samples

Most existing multivariate equivalence and superiority tests have been developed for two-sample settings, while methods for one-sample settings remain scarce. Moreover, most multivariate superiority tests combine superiority and non-inferiority tests rather than providing a purely one-sided test of joint superiority. To fill these gaps, we adapt the existing Intersection-Union Test and propose Likelihood Ratio Nonparametric and Parametric Bootstrap Tests for paired multivariate equivalence and component-wise superiority testing. Simulation studies demonstrate the ability of the proposed approach to detect equivalence and component-wise superiority while maintaining control of type I error rates. An application to real data further illustrates the practical utility of the approach. Overall, combining classical likelihood methods with bootstrap resampling yields a powerful and flexible solution for paired multivariate equivalence and component-wise superiority testing.