Efficient estimation in marginal partially linear models for longitudinal/clustered data using splines

We consider marginal semiparametric partially linear models for longitudinal/clustered data, where the models are specified totally by conditional moment restrictions. We derive the semiparametric efficient score function and information bound for this problem without an assumption of multivariate Gaussian errors. We propose an estimation procedure based on a spline approximation of the nonparametric part of the model and an extension of the parametric marginal generalized estimating equations (GEE). It is shown that our estimator of the parametric part of the model is asymptotically normal and achieves the semiparametric efficiency bound when the correct covariance structure is specified. Our estimator of the nonparametric part of the model is consistent and the rate of convergence is given. The proposed estimator effectively takes into account the within-subject/cluster correlation and is straightforward to implement.