Asymptotic Properties and Inferences for Varying Coefficient Regression with Longitudinal Variables

• Activity Number: 113
• Type: Contributed
• Date/Time: Monday, August 9, 2004 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Weishi Yuan*+ and Colin O. Wu
• Companies: Duke University and National Heart, Lung, and Blood Institute
• Keywords: regression ; varying coefficient ; longitudinal data ; cross-validation ; simulations

Abstract

Longitudinal data usually involve repeated measurements from a set of randomly chosen subjects, and this type of data frequently appears in biomedical and epidemiological studies. An important objective of statistical analyses with this type of data is to evaluate the effects of the covariates, which may or may not depend on time, on the time-varying response variable of interest. A well-developed regression methodology could have important practical impacts in evaluating new medical treatment, identifying influential risk factors, verifying existing biological models, etc. The varying-coefficient model is a structural nonparametric model that is particularly useful in exploring the time trend and associations between longitudinal outcomes and covariates. We investigate here a class of two-step smoothing methods based on covariate centering for estimating the coefficient curves in a linear time-varying coefficient model with time-dependent covariates. A cross-validation criterion is used to select the smoothing parameters. Methods for statistical inferences are suggested based on the asymptotic distributions of the estimators or a bootstrap procedure.