Speaker
Description
Quadratic forms, such as the rank-based Wald-type statistic or the rank-based ANOVA-type statistic, are widely used to compare multivariate distributions without the necessity of parametric assumptions (like multivariate normality). These tests have two major limitations, however:
i) They are, by construction, omnibus tests and thus not able to locate which specific dimensions (variables) are driving an indicated overall difference between the distributions.
ii) They fundamentally require the sample size to be much larger than the dimensionality of the data for reliable asymptotic inference.
The latter is particularly challenging in applications where there are many outcomes but only a few independent observations, such as genomics, rare disease studies, and pre-clinical studies.
In contrast, maximum statistics avoid aggregating squared differences across dimensions and instead focus on the single largest studentized difference. This structure provides local test results and therefore identifies which dimensions are driving an indicated difference, overcoming limitation i) above. In addition, they can provide simultaneous confidence intervals.
Nevertheless, maximum tests remain subject to limitation ii) above: standard inference based on the asymptotic distribution requires the sample size to be much larger than the dimensionality of the data.
In this talk, we propose a multiplier (wild) bootstrap with Rademacher weights to approximate the distribution of a maximum rank-based statistic. Specifically, we consider the classic comparison of distribution functions (Wilcoxon-Mann-Whitney test statistics) as well as the more flexible comparison of relative effects (Brunner-Munzel test statistics). We employ different standard error specifications for the corresponding test statistics and discuss their performance in terms of Type I error control and Type II error control in a comprehensive simulation study.
75002902684