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

TL;DR

This paper evaluates the power of various goodness-of-fit and two-sample tests for multivariate data through extensive simulations, recommending a small set of methods with reliable performance across scenarios.

Contribution

It provides comprehensive simulation results and proposes a selection of methods that maintain good power across different multivariate testing scenarios.

Findings

No single test is best for all cases.

A small set of methods can ensure good power across scenarios.

Simulations used R packages MD2sample and MDgof from CRAN.

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.