A Two-Sample Test for Equality of Means in High Dimension

Area of Science:

• Statistics
• Biostatistics
• Genomics

Background:

• Classic Hotelling T-squared test fails in "large-p-small-n" settings due to rank deficiency.
• Comparing population mean vectors is crucial in various scientific fields.

Purpose of the Study:

• Develop a robust test statistic for equality of two population mean vectors in "large-p-small-n" scenarios.
• Address limitations of existing methods, particularly with high-dimensional data.

Main Methods:

• Propose a "generalized component test" that avoids full covariance matrix estimation.
• Leverage a logical ordering of components and displacement-based dependence.
• The test is robust to heteroscedasticity and does not assume equal covariance matrices.

Main Results:

• The generalized component test demonstrates competitive performance against existing methods.
• Achieves superior statistical power for heavy-tailed data.
• Requires minimal computation time, suitable for very large datasets.

Conclusions:

• The generalized component test offers a powerful and efficient solution for high-dimensional mean vector comparisons.
• Applicable to diverse biological datasets, including mitochondrial function and cancer genomics.
• Provides a valuable tool for researchers in statistics and related sciences.