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Adaptive orthogonal series estimation in additive stochastic regression models
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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.Adaptive estimation; additive model; dependent process; mixing condition; nonlinear time series; nonparametric regression; orthogonal series; strict stationarity; truncation parameter