Adaptive orthogonal series estimation in additive stochastic regression models

摘要

In this paper, we consider additive stochastic nonparametric regression models. By approximating the nonparametric components by a class of orthogonal series and using a generalized cross-validation criterion, an adaptive and simultaneous estimation procedure for all the nonparametric components is constructed. We illustrate the adaptive and simultaneous estimation procedure by a number of simulated and real examples.