Accounting for Correlation in Semiparametric and Nonparametric Regression for Longitudinal Data

• Activity Number: 131
• Type: Invited
• Date/Time: Monday, August 12, 2002 : 2:00 PM to 3:50 PM
• Sponsor: ENAR
• Author(s): Raymond Carroll*+ and Naisyin Wang and Alan Welsh and Xihong Lin
• Affiliation(s): Texas A&M University and Texas A&M University and University of Southampton and University of Michigan
• Keywords: Splines ; Functional Regression ; Kernel Methods ; Semiparametrics ; Generalized Least Squares

Abstract

We discuss the problem of nonparametric regression and semiparametric regression for clustered data, including longitudinal studies. Most methods in the literature ignore the correlation structure entirely in estimation, taking a GEE-type approach with independence as the working correlation matrix.

Some kernel-based methods are known to perform poorly when they try to take advantage of the correlation structure; some are even worse than if the correlation structure were ignored entirely! It has been an open problem, whether it is possible to construct kernel methods which can take advantage of correlation in longitudinal and clustered-data studies.

Based on the work of Naisyin Wang, we will describe new kernel methods that account for correlation efficiently. We show that they are asymptotically equivalent to generalized least squares spline-based methods, both for nonparametric regression and for semiparametric regression. The construction leads to kernel and spline methods that are semiparametric-efficient for the partially linear model.