We consider efficient estimation of the Euclidean parameters in a generalized
partially linear additive models for longitudinal/clustered data when multiple
covariates need to be modeled nonparametrically, and propose an estimation
procedure based on a spline approximation of the nonparametric part of the
model and the generalized estimating equations (GEE). Although the model in
consideration is natural and useful in many practical applications, the
literature on this model is very limited because of challenges in dealing with
dependent data for nonparametric additive models. We show that the proposed
estimators are consistent and asymptotically normal even if the covariance
structure is misspecified. An explicit consistent estimate of the asymptotic
variance is also provided. Moreover, we derive the semiparametric efficiency
score and information bound under general moment conditions. By showing that
our estimators achieve the semiparametric information bound, we effectively
establish their efficiency in a stronger sense than what is typically
considered for GEE. The derivation of our asymptotic results relies heavily on
the empirical processes tools that we develop for the longitudinal/clustered
data. Numerical results are used to illustrate the finite sample performance of
the proposed estimators.Comment: Published in at http://dx.doi.org/10.3150/12-BEJ479 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
