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We consider efficient estimation of the Euclidean parameters in a generalizedpartially linear additive models for longitudinal/clustered data when multiplecovariates need to be modeled nonparametrically, and propose an estimationprocedure based on a spline approximation of the nonparametric part of themodel and the generalized estimating equations (GEE). Although the model inconsideration is natural and useful in many practical applications, theliterature on this model is very limited because of challenges in dealing withdependent data for nonparametric additive models. We show that the proposedestimators are consistent and asymptotically normal even if the covariancestructure is misspecified. An explicit consistent estimate of the asymptoticvariance is also provided. Moreover, we derive the semiparametric efficiencyscore and information bound under general moment conditions. By showing thatour estimators achieve the semiparametric information bound, we effectivelyestablish their efficiency in a stronger sense than what is typicallyconsidered for GEE. The derivation of our asymptotic results relies heavily onthe empirical processes tools that we develop for the longitudinal/clustereddata. Numerical results are used to illustrate the finite sample performance ofthe proposed estimators.

Efficient semiparametric estimation in generalized partially linear additive models for longitudinal/clustered data