Lan Xue, Oregon State University
We propose a 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 the local-region information for the 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 on the local region is more scientifically relevant than those on the entire region. However, this brings challenges in theoretical development due to high-dimensional parameters involved in nonparametric functions to capture the local information, in addition to computationally 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 selection approaches. The proposed method is also illustrated through the longitudinal growth and health study from National Heart, Lung and Blood Institute.
