Efficient semiparametric marginal estimation for longitudinal/clustered data

We consider marginal generalized semiparametric partially linear models for clustered data. Lin and Carroll derived the semiparametric efficient score function for this problem in the multivariate Gaussian case, but they were unable to construct a semiparametric efficient estimator that actually achieved the semiparametric information bound. Here we propose such an estimator and generalize the work to marginal generalized partially linear models. We investigate asymptotic relative efficiencies of the estimators that ignore the within-cluster correlation structure either in nonparametric curve estimation or throughout. We evaluate the finite-sample performance of these estimators through simulations and illustrate it using a longitudinal CD4 cell count dataset. Both theoretical and numerical results indicate that properly taking into account the within-subject correlation among the responses can substantially improve efficiency.