Simulation-based hypothesis testing of high dimensional means under covariance heterogeneity

Area of Science:

• Statistics
• Bioinformatics
• Genomics

Background:

• High-dimensional data analysis presents challenges in testing mean vectors.
• Existing methods often impose restrictive assumptions on covariance matrix structures.
• There is a need for robust tests applicable to general covariance structures.

Purpose of the Study:

• To develop novel statistical tests for one-sample and two-sample mean vector problems in high-dimensional data.
• To propose methods that accommodate general covariance structures, enhancing practical applicability.
• To improve the power of tests against sparse alternatives through feature screening.

Main Methods:

• Utilizing maximum-type statistics and parametric bootstrap techniques for critical value computation.
• Developing two-step procedures incorporating preliminary feature screening.
• Investigating the theoretical properties of the proposed testing procedures.

Main Results:

• The proposed tests demonstrate wide applicability due to relaxed assumptions on covariance matrices.
• Two-step procedures show enhanced power against sparse alternatives.
• Numerical experiments validate the performance on synthetic and real-world gene expression data.

Conclusions:

• The new tests provide a robust and widely applicable framework for high-dimensional mean vector testing.
• The methods aid in identifying disease-associated gene sets, particularly with sparse alternatives.
• An R-package, HDtest, is available for practical implementation.