Bayesian Sparse Learning of Joint Quantile Planes Estimation

Abstract

Although there has been a lot of research on the joint estimation of non-crossing quantile planes, methods of conducting sparse learning within this framework are still inadequate. In this thesis, we first briefly review a joint estimation framework which serves as the cornerstone. We then discuss the notion of sparsity of investigators’ interests and introduce a complete Bayesian sparse learning methodology to regularize function-valued parameters. We carry out extensive simulations to compare modeling with/without sparse learning implemented. Results from simulations show that our new sparse learning method outperforms in capturing either local or global sparsity. We also report a case study on the association of beta-carotene plasma concentrations with dietary intakes and drugs use for non-melanoma skin cancer patients.