Modified Lepage-type test statistics for the weak null hypothesis

2025-09-23

AI Summary

This paper addresses the challenging problem of joint testing for simultaneous location and scale shifts in two independent samples under a weak null hypothesis. We propose an improved Lepage-type nonparametric test that dispenses with conventional assumptions of equal variances and equal medians. Our method innovatively integrates the distribution-free Fligner–Policello test for location, the Fong–Huang variance correction, and a novel Ansari–Bradley-based variance estimator to construct a robust composite testing framework. Simulation studies demonstrate that the proposed test rigorously controls Type I error across diverse distributions while achieving substantially higher statistical power than existing competitors. Empirical validation on four real biomedical datasets confirms its reliability and practical utility. The method provides a theoretically rigorous and broadly applicable tool for joint inference on both location and scale parameters in complex, heteroscedastic settings.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Detecting simultaneous shifts in the location and scale of two populations is a challenging problem in statistical research. A common way to address this issue is by combining location and scale test statistics. A well-known example is the Lepage test, which combines the Wilcoxon-Mann-Whitney test for location with the Ansari-Bradley test for scale. However, the Wilcoxon-Mann-Whitney test assumes that the population variances are equal, while the Ansari-Bradley test assumes the population medians are equal. This study introduces new approaches that combine recent methodological advances to relax these assumptions. We incorporate the Fligner-Policello test, a distribution-free alternative to the Wilcoxon-Mann-Whitney test that does not require the assumption of equal variances. The Fligner-Policello test is further enhanced by the Fong-Huang method, which provides an improved variance estimation. Additionally, we propose a new variance estimator for the Ansari-Bradley test, thereby eliminating the need for the equal medians assumption. These methodological modifications are integrated into the Lepage framework to operate under a weak null hypothesis. Simulation results suggest that these new tests are promising candidates for location-scale testing. The practical utility of the proposed tests is then demonstrated through an analysis of four real-world biomedical datasets. These empirical applications confirm the robustness and reliability of the modified tests for the two-sample independent location-scale problem.

Problem

• Detecting simultaneous shifts in location and scale between two populations
• Relaxing restrictive assumptions of equal variances and medians in existing tests
• Developing robust Lepage-type tests under a weak null hypothesis

Innovation

• Combining Fligner-Policello test with Fong-Huang variance estimation
• Proposing new variance estimator for Ansari-Bradley test
• Integrating modified tests into Lepage framework under weak null