Quantile-based MANOVA: A new tool for inferring multivariate data in factorial designs

TL;DR

This paper introduces a robust multivariate analysis method based on quantiles, especially the median, for factorial designs, providing a flexible alternative to classical MANOVA that relies less on restrictive assumptions.

Contribution

It develops a novel quantile-based MANOVA approach applicable to all factorial designs, extending multivariate analysis with robustness and asymptotic validity.

Findings

Method is asymptotically valid for all factorial designs.

Simulation studies show good performance for small and moderate samples.

Applied to real data demonstrating practical utility.

Abstract

Multivariate analysis-of-variance (MANOVA) is a well established tool to examine multivariate endpoints. While classical approaches depend on restrictive assumptions like normality and homogeneity, there is a recent trend to more general and flexible proce dures. In this paper, we proceed on this path, but do not follow the typical mean-focused perspective. Instead we consider general quantiles, in particular the median, for a more robust multivariate analysis. The resulting methodology is applicable for all kind of factorial designs and shown to be asymptotically valid. Our theoretical results are complemented by an extensive simulation study for small and moderate sample sizes. An illustrative data analysis is also presented.