Longitudinal and Clustered Data and Non/Semiparametric Regression 

Raymond Carroll
Texas A&M University

I will review the problem of nonparametric and semiparametric regression for longitudinal/clustered data. In the independent data case, kernel methods are spline methods are essentially asymptotically equivalent for these problems. The same is not true for the longitudinal/clustered data case, with standard kernel methods failing to account for correlation in any sort of effective form. Indeed, such kernel methods and spline methods have different local influence functions (ëffective kernels"). A method due to Naisyin Wang resolves the dilemma: we indicate its use in semiparametric regression, and also its asymptotic equivalence with splines. 

Note: Joint work with Xihong Lin, Naisyin Wang and Alan Welsh.