Testing the Mean Matrix in High-Dimensional Transposable Data

TL;DR

This paper introduces a nonparametric, computationally efficient test for assessing mean matrix structures in high-dimensional transposable data, effectively handling dependence among variables.

Contribution

It develops a novel testing procedure for mean matrix structures that is powerful and maintains nominal size, applicable to gene expression data.

Findings

Good performance in simulations

Maintains nominal size

Effective in gene expression analysis

Abstract

The structural information in high-dimensional transposable data allows us to write the data recorded for each subject in a matrix such that both the rows and the columns correspond to variables of interest. One important problem is to test the null hypothesis that the mean matrix has a particular structure without ignoring the potential dependence structure among and/or between the row and column variables. To address this, we develop a simple and computationally efficient nonparametric testing procedure to assess the hypothesis that, in each predefined subset of columns (rows), the column (row) mean vector remains constant. In simulation studies, the proposed testing procedure seems to have good performance and unlike traditional approaches, it is powerful without leading to inflated nominal sizes. Finally, we illustrate the use of the proposed methodology via two empirical examples from gene expression microarrays.