  In this paper, we study the estimation for a partial-linear single-index
model. A two-stage estimation procedure is proposed to estimate the link
function for the single index and the parameters in the single index, as well
as the parameters in the linear component of the model. Asymptotic normality is
established for both parametric components. For the index, a constrained
estimating equation leads to an asymptotically more efficient estimator than
existing estimators in the sense that it is of a smaller limiting variance. The
estimator of the nonparametric link function achieves optimal convergence
rates; and the structural error variance is obtained. In addition, the results
facilitate the construction of confidence regions and hypothesis testing for
the unknown parameters. A simulation study is performed and an application to a
real dataset is illustrated. The extension to multiple indices is briefly
sketched.
