Statistical inference for quantile correlation regression with bivariate outcomes
Abstract
It is increasing scientifically important to recognize, quantify and visualize the dependence structure between the bivariate outcomes. In this paper, we investigate conditional dependence using a new dependence measure, the quantile correlation coefficient, which is defined by the Pearson correlation of two quantile-hits of bivariate outcomes. Furthermore, we propose a new regression model for covariate effects directly on the quantile correlation coefficient via a generalized linear regression model. The proposed model has intuitive interpretation and provides a comprehensive view of covariate effects across quantiles of bivariate outcomes. The proposed estimator enjoys desirable asymptotic properties including uniform consistency and weak convergence as a process in the quantile index. Additionally, we develop the general hypothesis testing for the regression coefficients, with applications to summarize covariate effects across the quantile ranges. Simulation studies demonstrate the good finite sample performance of the proposed estimation and inference procedures. Two empirical applications of the proposed method reveal interesting insights in premature twins data for measuring association and ChIP-seq data for measuring reproducibility.
Related
- Quantile-Only Regression: Inference and Partial Identification under Quantile Disclosure
- Statistical Inference for Bivariate Functional Causal Discovery
- Distributed Selective Inference for Quantile Regression
- Bias Correction and Inference for Panel Quantile Regression
- Finite-Sample Distribution Theory and Efficient Large-Scale Inference for Online Quantile Regression
BibTeX
@misc{zhang2026statistical,
title = {{Statistical inference for quantile correlation regression with bivariate outcomes}},
author = {Feipeng Zhang and Heng Peng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41126},
eprint = {2610.41126},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41126},
}
RIS
TY - UNPB
TI - Statistical inference for quantile correlation regression with bivariate outcomes
AU - Feipeng Zhang
AU - Heng Peng
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41126
UR - https://arxiv.org/abs/2610.41126
AB - It is increasing scientifically important to recognize, quantify and visualize the dependence structure between the bivariate outcomes. In this paper, we investigate conditional dependence using a new dependence measure, the quantile correlation coefficient, which is defined by the Pearson correlation of two quantile-hits of bivariate outcomes. Furthermore, we propose a new regression model for covariate effects directly on the quantile correlation coefficient via a generalized linear regression model. The proposed model has intuitive interpretation and provides a comprehensive view of covariate effects across quantiles of bivariate outcomes. The proposed estimator enjoys desirable asymptotic properties including uniform consistency and weak convergence as a process in the quantile index. Additionally, we develop the general hypothesis testing for the regression coefficients, with applications to summarize covariate effects across the quantile ranges. Simulation studies demonstrate the good finite sample performance of the proposed estimation and inference procedures. Two empirical applications of the proposed method reveal interesting insights in premature twins data for measuring association and ChIP-seq data for measuring reproducibility.
ER -