The Comparison of Nonparamteric Smoothing Methods for Longitudinal Data

There are many nonparametric estimation methods for the mean functions of marginal models for longitudinal data. Those estimators such as regression spline, smoothing spline and seemingly unrelated(SUR) kernel estimators can achieve the minimum asymptotic variance when the true covariance structure is specified. The asymptotic bias of the regression spline estimator does not depend on the working covariance matrix, but the asymptotic bias of smoothing spline and SUR kernel estimators depend on the working covariance matrix in a complicate manner. In this paper, we focus on the comparison of the estimation efficiency among the regression spline, smoothing spline and SUR kernel estimators. By simulation study, it is found that the regression spline estimator generally present higher efficiency than the other two estimators with smaller mean square errors.