  In this paper we propose a general series method to estimate a semiparametric
partially linear varying coefficient model. We establish the consistency and
\sqrtn-normality property of the estimator of the finite-dimensional parameters
of the model. We further show that, when the error is conditionally
homoskedastic, this estimator is semiparametrically efficient in the sense that
the inverse of the asymptotic variance of the estimator of the
finite-dimensional parameter reaches the semiparametric efficiency bound of
this model. A small-scale simulation is reported to examine the finite sample
performance of the proposed estimator, and an empirical application is
presented to illustrate the usefulness of the proposed method in practice. We
also discuss how to obtain an efficient estimation result when the error is
conditional heteroskedastic.
