This paper considers series estimators of additive interactive regression (AIR) models. AIR models are nonparametric regression models that generalize additive regression models by allowing interactions between diﬀerent regressor variables. They place more restrictions on the regression function, however, than do fully nonparametric regression models. By doing so, they attempt to circumvent the curse of dimensionality that aﬀlicts the estimation of fully nonparametric regression models. In this paper, we present a ﬁnite sample bound and asymptotic rate of convergence results for the mean average squared error of series estimators that show the AIR models do circumvent the curse of dimensionality. The rate of convergency of these estimators is shown to depend on the order of the AIR model and the smoothness of the regression function, but not on the dimension of the regressor vector. Series estimators with ﬁxed and data-dependent truncation parameters are considered.
Andrews, Donald W.K. and Whang, Yoon-Jae, "Additive Interactive Regression Models: Circumvention of the Curse of Dimensionality" (1989). Cowles Foundation Discussion Papers. 1169.