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Full-Text Articles in Social and Behavioral Sciences
Additive Interactive Regression Models: Circumvention Of The Curse Of Dimensionality, Donald W.K. Andrews, Yoon-Jae Whang
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 …
Asymptotics For Semiparametric Econometric Models: I. Estimation, Donald W.K. Andrews
Asymptotics For Semiparametric Econometric Models: I. Estimation, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper provides a general framework for proving the square root of T consistency and asymptotic normality of a wide variety of semiparametric estimators. The results apply in time series and cross-sectional modeling contexts. The class of estimators considered consists of estimators that can be defined as the solution to a minimization problem based on a criterion function that may depend on a preliminary infinite dimensional nuisance parameter estimator. The criterion function need not be differentiable. The method of proof exploits results concerning the stochastic equicontinuity or weak convergence of normalized sums of stochastic processes. This paper also considers tests …