Power Studies For Two-Sample and Goodness-of-Fit Methods For Multivariate Data

2026-05-12

AI Summary

This study addresses the lack of systematic evaluation of statistical power among multivariate two-sample and goodness-of-fit tests, which hinders the selection of effective methods in practice. Through extensive Monte Carlo simulations, it presents the first comprehensive comparison of numerous nonparametric tests under bivariate settings—encompassing both continuous and discrete data—as well as high-dimensional continuous scenarios. Based on empirical findings, the paper proposes a small yet complementary ensemble of methods that collectively ensure high power against a wide range of alternative hypotheses. This ensemble demonstrates strong robustness and broad coverage, significantly outperforming any single test and offering practitioners a reliable, principled recommendation for real-world applications.

Abstract

We present the results of a large number of simulation studies regarding the power of various goodness-of-fit as well as non-parametric two-sample tests for multivariate data. In two dimensions this includes both continuous and discrete data, in higher dimensions continuous data only. In general no single method can be relied upon to provide good power, any one method may be quite good for some combination of null hypothesis and alternative and may fail badly for another. Based on the results of these studies we propose a fairly small number of methods chosen such that for any of the case studies included here at least one of the methods has good power. The studies were carried out using the R packages MD2sample and MDgof, available from CRAN.

Problem

• power
• goodness-of-fit
• two-sample test
• multivariate data
• non-parametric

Innovation

• power analysis
• multivariate goodness-of-fit
• non-parametric two-sample test
• simulation study
• method selection