Varying-coefficients for regional quantile via KNN-based LASSO with
  applications to health outcome study
Seyoung Park Eun Ryung Lee Hyokyoung G. Hong
Health outcomes, such as body mass index and cholesterol levels, are known to
be dependent on age and exhibit varying effects with their associated risk
factors. In this paper, we propose a novel framework for dynamic modeling of
the associations between health outcomes and risk factors using
varying-coefficients (VC) regional quantile regression via K-nearest neighbors
(KNN) fused Lasso, which captures the time-varying effects of age. The proposed
method has strong theoretical properties, including a tight estimation error
bound and the ability to detect exact clustered patterns under certain
regularity conditions. To efficiently solve the resulting optimization problem,
we develop an alternating direction method of multipliers (ADMM) algorithm. Our
empirical results demonstrate the efficacy of the proposed method in capturing
the complex age-dependent associations between health outcomes and their risk
factors.