Semiparametric Time-varying Coefficients Regression Model for Longitudinal Data

• Activity Number: 40
• Type: Invited
• Date/Time: Sunday, August 7, 2005 : 4:00 PM to 5:50 PM
• Sponsor: ENAR
• Author(s): Yanqing Sun*+ and Hulin Wu
• Companies: University of North Carolina, Charlotte and University of Rochester
• Keywords: Asymptotic efficiency ; asymptotic optimal bandwidth ; hypothesis testing ; kernel smoothing ; single nearest neighbor smoothing ; uniform confidence bands

Abstract

In this paper, we consider a semiparametric time-varying coefficients regression model where the influences of some covariates vary nonparametrically with time, while the effects of the remaining covariates follow certain parametric functions of time. The weighted least squares type estimators for the unknown parameters of the parametric coefficient functions as well as the estimators for the nonparametric coefficient functions are developed. We show that the kernel smoothing, which avoids modeling of the sampling times, is asymptotically more efficient than a single nearest neighbor smoothing, which depends on the estimation of the sampling model. The asymptotic optimal bandwidth also is derived. A hypothesis-testing procedure is proposed to test whether some covariate effects follow certain parametric forms. Simulation studies are conducted to compare the finite sample performances of the kernel neighborhood smoothing and the single nearest neighbor smoothing as well as to check the empirical sizes and powers of the proposed testing procedures. An application to a dataset from an AIDS clinical trial study is provided for illustration.