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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 …
Asymptotic Optimality Of Generalized Cl, Cross-Validation, And Generalized Cross-Validation In Regression With Heteroskedastic Errors, Donald W.K. Andrews
Asymptotic Optimality Of Generalized Cl, Cross-Validation, And Generalized Cross-Validation In Regression With Heteroskedastic Errors, Donald W.K. Andrews
Cowles Foundation Discussion Papers
The problem considered here is that of using a data-driven procedure to select a good estimate from a class of linear estimates indexed by a discrete parameter. In contrast to other papers on this subject, we consider models with heteroskedastic errors. The results apply to model selection problems in linear regression and to nonparametric regression estimation via series estimators, nearest neighbor estimators, and local regression estimators, among others. Generalized C L , cross-validation, and generalized cross-validation procedures are analyzed.