Reduced varying coefficient models for regional quantile regression with multiple responses.

Area of Science:

• Statistics
• Biostatistics
• Machine Learning

Background:

• High-dimensional data analysis presents statistical and computational challenges, particularly for multivariate quantile regression.
• Existing methods struggle to model complex, quantile-specific associations across multiple outcomes efficiently.

Purpose of the Study:

• To develop a novel statistical framework for analyzing multivariate quantile varying coefficients in high-dimensional settings.
• To enhance parsimony and interpretability by enforcing a low-rank structure on coefficient matrices.
• To identify latent structures and shared patterns within principal components using KNN-fused LASSO.

Main Methods:

• A new framework modeling multivariate quantile varying coefficients using principal component functions.
• Enforcement of a low-rank structure on the coefficient matrix for parsimony.
• Augmentation with a KNN-fused LASSO penalty for pattern identification and clustering.

Main Results:

• Comprehensive simulations demonstrate accurate estimation and robust performance in various high-dimensional scenarios.
• The method successfully uncovers complex, quantile-specific associations between predictors and multiple correlated outcomes.
• Application to real-world health datasets highlights practical utility and discovery of intricate associations.

Conclusions:

• The proposed framework offers an effective solution for multivariate quantile regression in high-dimensional data.
• The method achieves parsimony and interpretability while capturing dynamic patterns and latent structures.
• This approach has significant implications for analyzing complex health outcomes and identifying predictive relationships.