FarmTest

FarmTest provides factor-adjusted robust multiple testing for large-scale correlated and heavy-tailed data to control the false discovery proportion (FDP) and improve statistical power.

Key Features:

• Robustness to Heavy-Tailed Data: Handles heavy-tailed distributions in test statistics to produce reliable estimation under non-Gaussian tails.
• Control of False Discovery Proportion (FDP): Implements procedures to control the false discovery proportion (FDP) while enhancing power via factor adjustment.
• Factor Adjustments: Adjusts for latent factors that influence test statistics to reduce bias in multiple testing.
• Independence from Joint Normality Assumptions: Operates without assuming joint normality of observations, accommodating broader dependence structures.
• Consistency in Estimation: Provides consistent FDP estimation under general conditions.
• Exponential-Type Deviation Inequality: Establishes an exponential-type deviation inequality for a robust U-type covariance estimator under the spectral norm.

Scientific Applications:

• Genomics: Analyzing gene expression and other genomic data with correlated and heavy-tailed measurements.
• Medical Imaging: Detecting significant patterns in medical imaging datasets with complex dependencies.
• Finance: Analyzing market and financial data that exhibit heavy tails and dependencies for multiple hypothesis testing.

Methodology:

Robust factor adjustments, a robust U-type covariance estimator analyzed via an exponential-type deviation inequality under the spectral norm, and procedures for FDP control without assuming joint normality.