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Additive Interactive Regression Models: Circumvention Of The Curse Of Dimensionality, Donald W.K. Andrews, Yoon-Jae Whang

Cowles Foundation Discussion Papers

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 …