Department of Statistics Seminar
North Carolina State University

presents

Dr. Xihong Lin

University of Michigan

"Nonparametric and Semiparametric Regression For Clustered/Longitudinal Data Using Kernel and Spline Methods"

ABSTRACT

We consider nonparametric and semiparametric regression estimation for clustered/longitudinal data using kernel and (smoothing and regression) spline methods. A key feature of the smoothing spline method is that it can be fit using mixed models. However, its properties have not been well understood. For independent data, it is well known that kernel methods and smoothing spline methods are essentially asymptotically equivalent (Silverman, 1984). However, it is found recently that the same is not true for clustered/longitudinal data. Conventional kernel methods fail to account for the within-cluster correlation and are local, while spline methods are able to account for this correlation and are nonlocal. We show that a smoothing spline estimator is asymptotically equivalent to a newly proposed seemingly unrelated (SUR) kernel estimator. The most efficient spline and SUR kernel estimators are obtained by accounting for the within-cluster correlation and are nonlocal, but have asymptotically negligible bias. Our results justify the use of efficient, nonlocal estimators such as smoothing clustered/longitudinal data. We extend the results to semiparametric regression models, where some covariate effects are modeled parametrically, while others are modeled nonparametrically. We derive the semiparametric efficient score and show the profile/kernel or spline estimator is semiparametric efficient. The results are illustrated using simulation studies and data examples.

Friday, March 7, 2003

3:35 - 4:35 pm

206 Cox Hall

Refreshments will be served on the second floor of Dabney Hall (left of Room 222) at 3:00 pm.