Exact Multivariate Tests - A New Effective Principle of Controlled Model Choice

TL;DR

This paper introduces a new principle for controlled model choice in high-dimensional multivariate testing, improving error control by reinterpreting hypotheses on distributional sphericity, with applications in bioinformatics.

Contribution

It offers a novel mathematical interpretation of multivariate tests that allows for better error control in model selection without strict restrictions.

Findings

Enhanced control of the first kind error in multivariate tests

Applicable to all linear multivariate designs

Illustrated with gene set selection in bioinformatics

Abstract

High-dimensional tests are applied to find relevant sets of variables and relevant models. If variables are selected by analyzing the sums of products matrices and a corresponding mean-value test is performed, there is the danger that the nominal error of first kind is exceeded. In the paper, well-known multivariate tests receive a new mathematical interpretation such that the error of first kind of the combined testing and selecting procedure can more easily be kept. The null hypotheses on mean values are replaced by hypotheses on distributional sphericity of the individual score responses. Thus, model choice is possible without too strong restrictions. The method is presented for all linear multivariate designs. It is illustrated by an example from bioinformatics: The selection of gene sets for the comparison of groups of patients suffering from B-cell lymphomas.