  This paper considers the problem of estimation in the generalized
semiparametric model for longitudinal data when the number of parameters
diverges with the sample size. A penalization type of generalized estimating
equation method is proposed, while we use the regression spline to approximate
the nonparametric component. The proposed procedure involves the specification
of the posterior distribution of the random effects, which cannot be evaluated
in a closed-form. However, it is possible to approximate this posterior
distribution by producing random draws from the distribution using a Metropolis
algorithm. Under some regularity conditions, the resulting estimators enjoy the
oracle properties, under the high-dimensional regime. Simulation studies are
carried out to assess the performance of our proposed method, and two real data
sets are analyzed to illustrate the procedure.
