Focused information criterion and model averaging for varying-coefficient partially linear models with longitudinal data

We study model selection and model averaging in varying-coefficient partially linear model with longitudinal data. The model is estimated by combining spline approximations and the generalized estimating equations. The corresponding linear coefficient estimators are shown to be asymptotically normal. Then we propose a focused information criterion and a frequentist model average estimator, and establish the asymptotic properties of the proposed estimators. Simulation studies show the proposed methods are superior to the existing ones even if the covariance structure is misspecified. The procedures are further applied to a real data case.