High-Dimensional U-Statistics Type Hypothesis Testing via Jackknife Pseudo-Values with Multiplier Bootstrap

Abstract

High-dimensional parameter testing is commonly used in bioinformatics to analyze complex relationships in gene expression and brain connectivity studies, involving parameters like means, covariances, and correlations. In this paper, we present a novel approach for testing U-statistics-type parameters by leveraging jackknife pseudo-values. Inspired by Tukey’s conjecture, we establish the asymptotic independence of these pseudo-values, allowing us to reformulate U-statistics-type parameter testing as a sample mean testing problem. This reformulation enables the use of established sample mean testing frameworks, simplifying the testing procedure. We apply a multiplier bootstrap method to obtain critical values and provide a rigorous theoretical analysis to validate the approach. Simulation studies demonstrate the robustness of our method across a variety of scenarios. Additionally, we apply our approach to investigate differences in the dependency structures of a subset of genes within the Wnt signaling pathway, which is associated with lung cancer.

Keywords

• high-dimensional
• hypothesis testing
• U-statistic
• jackknife
• multiplier bootstrap