We consider marginal generalized partially linear single-index models for
longitudinal data. A profile generalized estimating equations (GEE)-based approach
is proposed to estimate unknown regression parameters. Within a wide range of
bandwidths for estimating the nonparametric function, our profile GEE estimator is
consistent and asymptotically normal even if the covariance structure is misspeci-
fied. Moreover, if the covariance structure is correctly specified, the semiparametric
efficiency can be achieved under heteroscedasticity and without distributional assump-
tions on the covariates. Simulation studies are conducted to evaluate the finite sample
performance of the proposed procedure. The proposed methodology is further illus-
trated through a data analysis.

• Efficient estimation for marginal generalized partially linear single-index models with longitudinal data