Springer International Publishing AG 2017. This chapter considers the three-dimensional nonparametric models with random effects, and proposes pooled local linear and two-step estimators for them. We find that the pooled local linear estimator can be inconsistent when the sum of all the error term covariances in absolute values diverges to infinity too quickly. When the pooled local linear estimator is consistent, the optimal convergence rate of the estimator, its corresponding optimal bandwidth and asymptotic variance depend on the number of regressors and the limit of certain sample indices ratio; and we propose an asymptotically more efficient two-step estimator along the line of Su et al. (2013). Some extensions on nonparametric models with fixed effects, mixed effects, and higher dimensions are also discussed.
