  In this paper, we consider a single-index mixed model with longitudinal data.
A new set of estimating equations is proposed to estimate the single-index
coefficient. The link function is estimated by using the local linear
smoothing. Asymptotic normality is established for the proposed estimators.
Also, the estimator of the link function achieves optimal convergence rates;
and the estimators of variance components have root-$n$ consistency. These
results facilitate the construction of confidence regions/intervals and
hypothesis testing for the parameters of interest. Some simulations and an
application to real data are included.

Methodology