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Additive Interactive Regression Models: Circumvention of the Curse of Dimensionality

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Author Info
Andrews, Donald W.K.
Whang, Yoon-Jae

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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 non-parametric regression models.

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Publisher Info
Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 6 (1990)
Issue (Month): 04 (December)
Pages: 466-479
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Handle: RePEc:cup:etheor:v:6:y:1990:i:04:p:466-479_00

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Gallant, A. Ronald, 1981. "On the bias in flexible functional forms and an essentially unbiased form : The fourier flexible form," Journal of Econometrics, Elsevier, vol. 15(2), pages 211-245, February. [Downloadable!] (restricted)
  2. Andrews, Donald W K, 1991. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Econometrica, Econometric Society, vol. 59(2), pages 307-45, March. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Gordon B. Dahl, 2002. "Mobility and the Return to Education: Testing a Roy Model with Multiple Markets," RCER Working Papers 488, University of Rochester - Center for Economic Research (RCER). [Downloadable!]
  2. Oliver LINTON, . "Applied nonparametric methods," Statistic und Oekonometrie 9312, Humboldt Universitaet Berlin. [Downloadable!]
    Other versions:
  3. Oliver Linton & Yoon-Jae Whang, 2000. "Nonparametric Estimation with Aggregated Data," STICERD - Econometrics Paper Series /2000/397, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
    Other versions:
  4. Jing Wang & Lijian Yang, 2009. "Efficient and fast spline-backfitted kernel smoothing of additive models," Annals of the Institute of Statistical Mathematics, Springer, vol. 61(3), pages 663-690, September. [Downloadable!] (restricted)
  5. Donald W.K. Andrews, 1989. "Asymptotic Optimality of Generalized C_{L}, Cross-Validation, and Generalized Cross-Validation in Regression with Heteroskedastic Errors," Cowles Foundation Discussion Papers 906, Cowles Foundation, Yale University. [Downloadable!]
  6. Mitali Das, 2000. "Instrumental Variables Estimation of Nonparametric Models with Discrete Endogenous Regressors," Econometric Society World Congress 2000 Contributed Papers 1008, Econometric Society. [Downloadable!]
  7. Michael Hamers & Michael Kohler, 2006. "Nonasymptotic Bounds on the L 2 Error of Neural Network Regression Estimates," Annals of the Institute of Statistical Mathematics, Springer, vol. 58(1), pages 131-151, March. [Downloadable!] (restricted)
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