title: Domain selection for the varying coefficient model via local polynomial regression.
abstract: In this article, we consider the varying coefficient model, which allows the relationship between the predictors and response to vary across the domain of interest, such as time. In applications, it is possible that certain predictors only affect the response in particular regions and not everywhere. This corresponds to identifying the domain where the varying coefficient is nonzero. Towards this goal, local polynomial smoothing and penalized regression are incorporated into one framework. Asymptotic properties of our penalized estimators are provided. Specifically, the estimators enjoy the oracle properties in the sense that they have the same bias and asymptotic variance as the local polynomial estimators as if the sparsity is known as apriori. The choice of appropriate bandwidth and computational algorithms are discussed. The proposed method is examined via simulations and a real data example.
authors.affiliation: Department of Statistics, North Carolina State University.
authors.forename: Dehan
authors.initials: D
authors.lastname: Kong
authors.affiliation: Department of Statistics, North Carolina State University.
authors.forename: Howard
authors.initials: H
authors.lastname: Bondell
authors.affiliation: Department of Statistics, North Carolina State University.
authors.forename: Yichao
authors.initials: Y
authors.lastname: Wu
keywords: Bandwidth selection; Oracle properties; Penalized local polynomial fitting; SCAD