Two-stage efficient estimation of longitudinal nonparametric additive models

Nonparametric smoothings are useful tool to model longitudinal data. In this paper we study the estimating problem of longitudinal nonparametric additive regression models. A two-stage efficient approach is developed to estimate the unknown additive components. We show the resulted estimators have some advantages over the existed ones. For example, they are asymptotically more efficient than those neglecting the dependence of repeated observations over time within the same subject, have an oracle property, that is the asymptotic distribution of each additive component is the same as it would be if the other components were known with certainty, and can be naturally extended to deal with generalized longitudinal nonparametric additive regression model. The asymptotic normality is established for the underlying additive components. Some simulation studies are conducted to illustrate the finite sample performance of the proposed procedure. Applying the proposed procedure to a real data set is also made.