Multivariate equivalence and component-wise superiority tests for paired samples.

Area of Science:

• Statistics
• Biostatistics

Background:

• Existing multivariate equivalence and superiority tests are primarily for two-sample settings, with limited options for one-sample scenarios.
• Current multivariate superiority tests often conflate superiority and non-inferiority, lacking purely one-sided joint superiority tests.

Purpose of the Study:

• To address the scarcity of one-sample multivariate testing methods.
• To develop and validate novel statistical tests for paired multivariate equivalence and component-wise superiority.

Main Methods:

• Adaptation of the Intersection-Union Test.
• Development of Likelihood Ratio Nonparametric and Parametric Bootstrap Tests.
• Utilizing simulation studies and real-data application for validation.

Main Results:

• The proposed methods successfully detect multivariate equivalence and component-wise superiority.
• Type I error rates are effectively controlled in simulation studies.
• The approach demonstrates practical utility through real-data application.

Conclusions:

• The combined classical likelihood methods and bootstrap resampling offer a robust and adaptable solution.
• This work expands the toolkit for one-sample multivariate statistical testing.
• The developed tests are powerful for paired multivariate equivalence and component-wise superiority analysis.