Using Correlation in Smoothing Longitudinal Data

• Activity Number: 207
• Type: Topic Contributed
• Date/Time: Tuesday, August 13, 2002 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Derick Peterson*+ and Hongwei Zhao and Sara Eapen
• Affiliation(s): University of Rochester and University of Rochester and University of Rochester
• Keywords: Smooth ; Longitudinal ; Nonparametric ; Regression ; Correlated

Abstract

We consider the general problem of smoothing longitudinal data to estimate the nonparametric marginal mean function when a random but bounded number of measurements are available for each independent subject. In contrast to recent work in this area, we show that it is indeed possible to make good use of the correlation structure to improve precision. We propose a simple, explicit estimator that retains the asymptotic properties of the working independence local polynomial smoother, while besting its finite-sample performance when the average number of measurements per subject is not too small relative to the number of subjects. This behavior is demonstrated in a simulation. The class of local polynomial kernel-based estimating equations previously considered in the literature is shown to use the correlation structure in a clearly detrimental way, which explains why working independence was found to be the optimal member of this class. Finally, we show that ignoring the correlation structure necessarily results in inefficiency, as in the parametric setting; moreover, no local regression method is efficient in this model, and this inefficiency can, unfortunately, be substantial.