Marginal Non- and Semi-Parametric Regression for Longitudinal Data

Abstract

There has been a substantial recent interest in investigating the performance of non- and semiparametric marginal estimation using kernel methods. Most approaches adopt the strategy of ignoring the within-cluster correlation structure either in nonparametric curve estimation or throughout. When the cluster size m remains fixed, a result supporting the use of this "working independence" strategy indicates that under the conventional estimation procedure, a correct specification of the correlation structure actually diminishes the asymptotic efficiency. In this presentation, I will discuss an alternative kernel estimating equation that accounts for the within subject correlation. For nonparametric curve estimation, the variance of the proposed method is uniformly smaller than that of the most efficient working independence approach. Under the framework of marginal generalized partially linear models, the new estimator is semiparametric efficient in the Gaussian case, and is more efficient than the working independence estimator in non-- Gaussian cases. ( Joint work with Ray Carroll & Xihong Lin.)