Additive Interactive Regression Models: Circumvention of the Curse of Dimensionality

Donald Andrews () and Yoon-Jae Whang

No 925, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: 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.

Keywords: Additive interactive regression model; cross-validation; curse of dimensionality; generalized cross-validation; mean average squared error; nonparametric estimation; nonparametric regression; series estimator (search for similar items in EconPapers)
Pages: 20 pages
Date: 1989-09
Note: CFP 771.
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Citations: View citations in EconPapers (4)

Published in Econometric Theory (1990), 6: 455-479

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