Inference on multiple quantiles in regression models by a rank-score approach

2025-11-11

AI Summary

In multiple quantile regression, conventional multiple testing procedures fail to control the family-wise error rate (FWER) rigorously. To address this, we propose a multivariate joint test based on rank scores, embedded within a closed testing procedure to guarantee strong FWER control. This work constitutes the first extension of rank-score-based inference to simultaneous quantile regression, overcoming the low statistical power inherent in Bonferroni-type corrections. We establish the asymptotic validity of the proposed test under mild regularity conditions. Extensive Monte Carlo simulations demonstrate that the method maintains the nominal FWER level precisely across diverse simulation designs while delivering substantially higher statistical power than existing approaches.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

This paper tackles the challenge of performing multiple quantile regressions across different quantile levels and the associated problem of controlling the familywise error rate, an issue that is generally overlooked in practice. We propose a multivariate extension of the rank-score test and embed it within a closed-testing procedure to efficiently account for multiple testing. Theoretical foundations and simulation studies demonstrate that our method effectively controls the familywise error rate while achieving higher power than traditional corrections, such as Bonferroni.

Problem

• Developing multivariate rank-score test for multiple quantile regression
• Controlling familywise error rate across different quantile levels
• Enhancing statistical power compared to traditional correction methods

Innovation

• Multivariate rank-score test extension for quantile regression
• Closed-testing procedure controls familywise error rate
• Higher power achieved than traditional Bonferroni correction