Abstract: 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 the nonparametric components is constructed. We illustrate the adaptive and simultaneous estimation procedure by a number of simulated and real examples.
Key words and phrases: Adaptive estimation, additive model, dependent process, mixing condition, nonlinear time series, nonparametric regression, orthogonal series, strict stationarity, truncation parameter.