Efficient estimation for error component seemingly unrelated nonparametric regression models

Multivariate panel data provides a unique opportunity in studying the joint evolution of multiple response variables over time. In this paper, we propose an error component seemingly unrelated nonparametric regression model to fit the multivariate panel data, which is more flexible than the traditional error component seemingly unrelated parametric regression. By applying the undersmoothing technique and taking both of the correlations within and among responses into account, we propose an efficient two-stage local polynomial estimation for the unknown functions. It is shown that the resulting estimators are asymptotically normal, and have the same biases as the standard local polynomial estimators, which are only based on the individual response, and smaller asymptotic variances. The performance of the proposed procedure is evaluated through a simulation study and a real data set.