Partial Linear Model Averaging Prediction for Longitudinal Data

Prediction plays an important role in data analysis. Model averaging method generally provides better prediction than using any of its components. Even though model averaging has been extensively investigated under independent errors, few authors have considered model averaging for semiparametric models with correlated errors. In this paper, the authors offer an optimal model averaging method to improve the prediction in partially linear model for longitudinal data. The model averaging weights are obtained by minimizing criterion, which is an unbiased estimator of the expected in-sample squared error loss plus a constant. Asymptotic properties, including asymptotic optimality and consistency of averaging weights, are established under two scenarios: (i) All candidate models are misspecified; (ii) Correct models are available in the candidate set. Simulation studies and an empirical example show that the promise of the proposed procedure over other competitive methods.