A difficulty of nonparametric techniques is the curse of dimensionality. One cannot estimate nonparametrically in high dimensions unless restrictions are made. The present chapter considers a selection of such more restrictive models. The techniques are intermediate between purely parametric and purely nonparametric. Prime among these models are additive models and the closely related functional coefficient models. The nonparametric structure is then typically allowed to depend on just one or two variables at a time. There is also the possibility of letting a nonparametric term depend on a linear combination of variables as in the index models or in projection pursuit. Finally, there are semiparametric models, where some of the variables are modelled parametrically, some nonparametrically.
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