Reduced varying coefficient models for regional quantile regression with multiple responses

Analyzing multiple outcome variables via regional quantile regression in high-dimensional settings poses significant statistical and computational challenges. In this paper, we propose a new framework that models multivariate quantile varying coefficients using principal component functions, enforcing a low-rank structure on the coefficient matrix to achieve parsimony and interpretability. Our approach augments this representation with a KNN-fused LASSO penalty to capture shared dynamic patterns and identify latent clusters within the principal components. Through comprehensive simulation studies, we demonstrate that our method consistently provides accurate estimates and robust performance under various high-dimensional scenarios. We further illustrate its practical utility with two real-world health datasets, where our approach uncovers complex, quantile-specific associations between predictors and multiple correlated outcomes across a time index.