title: Shrinkage Estimation of Varying Covariate Effects Based On Quantile Regression.
abstract: Varying covariate effects often manifest meaningful heterogeneity in covariate-response associations. In this paper, we adopt a quantile regression model that assumes linearity at a continuous range of quantile levels as a tool to explore such data dynamics. The consideration of potential non-constancy of covariate effects necessitates a new perspective for variable selection, which, under the assumed quantile regression model, is to retain variables that have effects on all quantiles of interest as well as those that influence only part of quantiles considered. Current work onl1-penalized quantile regression either does not concern varying covariate effects or may not produce consistent variable selection in the presence of covariates with partial effects, a practical scenario of interest. In this work, we propose a shrinkage approach by adopting a novel uniform adaptive LASSO penalty. The new approach enjoys easy implementation without requiring smoothing. Moreover, it can consistently identify the true model (uniformly across quantiles) and achieve the oracle estimation efficiency. We further extend the proposed shrinkage method to the case where responses are subject to random right censoring. Numerical studies confirm the theoretical results and support the utility of our proposals.
authors.affiliation: Department of Biostatistics and Bioinformatics, Emory University, 1518 Clifton Rd. NE, Atlanta, USA.
authors.forename: Limin
authors.initials: L
authors.lastname: Peng
authors.affiliation: Department of Statistics and Applied Probability, National University of Singapore, Singapore 117546.
authors.forename: Jinfeng
authors.initials: J
authors.lastname: Xu
authors.affiliation: Department of Rehabilitation Medicine, Emory University, Atlanta, USA 30322.
authors.forename: Nancy
authors.initials: N
authors.lastname: Kutner
keywords: Adaptive-LASSO; Censoring; Quantile regression; Shrinkage estimation; Variable selection; Varying covariate effects