Abstract #300668

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JSM 2003 Abstract #300668
Activity Number: 344
Type: Invited
Date/Time: Wednesday, August 6, 2003 : 10:30 AM to 12:20 PM
Sponsor: Noether Award Committee
Abstract - #300668
Title: Nonparametric and Semiparametric Regression for Clustered/Longitudinal Data Using Kernel and Spline Methods
Author(s): Xihong Lin*+
Companies: University of Michigan
Address: 1420 Washington Heights, Ann Arbor, MI, 48109-2009,
Keywords: longitudinal data ; nonparametric regression ; semiparametric regression ; spline ; kernel ; GEE and mixed models
Abstract:

We consider nonparametric and semiparametric regression estimation for clustered/longitudinal data using kernel and spline methods. A key feature of the spline method is that it can be fit using mixed models. However, its properties are not well understood. For independent data, it is well-known that kernel methods and spline methods are essentially asymptotically equivalent (Silverman 1984). However, the recent work of Welsh, et al. (2002) shows that the same is not true for clustered/longitudinal data. First, conventional kernel methods fail to account for the within-cluster correlation, while spline methods are able to account for this correlation. Second, kernel methods and spline methods are found to have different local behaviors, with conventional kernels being local and splines being nonlocal. We show that a smoothing spline estimator is asymptotically equivalent to a newly proposed seemingly unrelated (SUR) kernel estimator for any working covariance matrix. The most efficient spline and SUR kernel estimators are obtained by accounting for the within-cluster correlation. We derive the asymptotic properties of smoothing splines.

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