Local Feature Selection in Varying Coefficient Models for Longtitudinal Data

• Activity Number: 435
• Type: Invited
• Date/Time: Wednesday, August 6, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Korean International Statistical Society
• Author(s): Lan Xue*+ and Xinxin Shu and Peibei Shi and Annie Qu
• Companies: Oregon State University and University of Illinois at Urbana-Champaign and University of Illinois at Urbana-Champaign and University of Illinois at Urbana-Champaign
• Keywords: Adaptive LASSO ; Group penalization ; Model selection ; Polynomial spline ; Quadratic inference function ; Truncated L1-penalty

Abstract

We propose new varying-coefficient model selection and estimation based on the spline approach which is capable of capturing time-dependent covariate effects. The new penalty function utilizes local-region information for varying coefficient estimation, in contrast to the traditional model selection approach focusing on the entire region. The proposed method is extremely useful when the signals associated with relevant predictors are time-dependent, and detecting relevant covariate effects in the local region is more scientifically relevant than those of the entire region. However, this brings challenges in theoretical development, due to the large-dimensional parameters involved in the nonparametric functions to capture the local information, in addition to computational challenges in solving optimization problems with overlapping parameters for different local-region penalization. We provide the asymptotic theory of model selection consistency on detecting local signals and establish the optimal convergence rate for the varying-coefficient estimator. Our simulation studies indicate that the proposed model selection incorporating local features outperforms the global feature model