Power Enhancement of Permutation-Augmented Partial-Correlation Tests via Fixed-Row Permutations

2025-06-03

AI Summary

Conventional permutation-based partial correlation tests suffer from severe power collapse under high collinearity among covariates. Method: This paper proposes a novel “fix-selected-rows—permute-remaining-rows” permutation strategy, which strictly controls Type-I error at the nominal level in finite samples under arbitrary fixed design matrices and exchangeable noise. Contribution/Results: The core innovation is a greedy algorithm that selects the optimal subset of rows to fix—maximizing a lower bound on statistical power—thereby mitigating spurious collinearity between covariates and the permutation structure. Theoretical analysis guarantees worst-case adherence to the nominal significance level. Simulation studies demonstrate substantial power gains over unconstrained permutation in high-collinearity settings, while maintaining robust error control.

Technology Category

Game Theory and Economic Paradigms: Imperfect InformationMachine Learning: Matrix & Tensor MethodsSearch and Optimization: Non-convex Optimization

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsSecurity and Privacy: Large-scale security measurementsEconomics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Permutation-based partial-correlation tests guarantee finite-sample Type I error control under any fixed design and exchangeable noise, yet their power can collapse when the permutation-augmented design aligns too closely with the covariate of interest. We remedy this by fixing a design-driven subset of rows and permuting only the remainder. The fixed rows are chosen by a greedy algorithm that maximizes a lower bound on power. This strategy reduces covariate-permutation collinearity while preserving worst-case Type I error control. Simulations confirm that this refinement maintains nominal size and delivers substantial power gains over original unrestricted permutations, especially in high-collinearity regimes.

Problem

• Enhances power of partial-correlation tests with fixed-row permutations
• Reduces covariate-permutation collinearity while controlling Type I error
• Improves test power in high-collinearity scenarios via greedy algorithm

Innovation

• Fixes design-driven rows, permutes remainder
• Uses greedy algorithm to maximize power
• Reduces collinearity, preserves error control