Work

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

Year: 2024

Type: article

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.

Source: Mathematics

DOI: 10.3390/math12233837

Authors: Mingjuan Zhang, Libin Jin

Institution: Shanghai Lixin University of Accounting and Finance

Language: English

Topic: Statistical Methods and Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,955

Funder: National Natural Science Foundation of China