Adaptive testing for association between two random vectors in moderate to high dimensions.

Area of Science:

• Statistics
• High-Dimensional Data Analysis
• Biostatistics

Background:

• Association testing is crucial across many scientific fields.
• Existing methods like Escoufier's RV test are limited to low-dimensional data.
• High-dimensional data often involves sparse associations, requiring specialized statistical approaches.

Purpose of the Study:

• To generalize the RV test for moderate-to-high dimensional data.
• To develop a data-adaptive test that accounts for sparse signals.
• To enhance association testing power in complex datasets.

Main Methods:

• Generalization of Escoufier's RV test using data-adaptive weighting of variable pairs.
• Development of an adaptive test robust to noise accumulation in high dimensions.
• Modification of the test for detecting nonlinear or nonmonotonic associations.

Main Results:

• The proposed adaptive test maintains statistical power for both dense and sparse associations.
• Demonstrated advantages over existing methods using real and simulated data.
• Established connections with generalized estimating equations, multivariate kernel machine regression, and kernel distance methods.

Conclusions:

• The new adaptive test offers a powerful and flexible solution for high-dimensional association analysis.
• The method is effective for various association types, including sparse and nonlinear.
• The test is publicly available in the R package aSPC for broader scientific application.