Average Regression Surface for Dependent

We study the estimation of the additive components in additive regression models, based on the weighted sample average of regression surface, for stationary-mixing processes. Explicit expression of this method makes possible a fast computation and allows an asymptotic analysis. The estimation procedure is especially useful for additive modeling. In this paper, it is shown that the average surface estimator shares the same optimality as the ideal estimator and has the same ability of estimating the additive component as the ideal case where other components are known. Formulas for the asymptotic bias and normality of the estimator are established.