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Additive Interactive Regression Models: Circumvention of the Curse of Dimensionality

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  • Andrews, Donald W.K.
  • Whang, Yoon-Jae

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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Bibliographic 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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  1. Andrews, Donald W K, 1991. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 307-45, March.
  2. Gallant, A. Ronald, 1981. "On the bias in flexible functional forms and an essentially unbiased form : The fourier flexible form," Journal of Econometrics, Elsevier, Elsevier, vol. 15(2), pages 211-245, February.
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Cited by:
  1. Mitali Das, 2000. "Instrumental Variables Estimation of Nonparametric Models with Discrete Endogenous Regressors," Econometric Society World Congress 2000 Contributed Papers 1008, Econometric Society.
  2. 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, Springer, vol. 58(1), pages 131-151, March.
  3. Hengartner, Nicolas W. & Sperlich, Stefan, 2005. "Rate optimal estimation with the integration method in the presence of many covariates," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 246-272, August.
  4. Wolfgang Hardle & Oliver Linton, 1994. "Applied Nonparametric Methods," Cowles Foundation Discussion Papers 1069, Cowles Foundation for Research in Economics, Yale University.
  5. Gordon Dahl, 1997. "Mobility and the Returns to Education: Testing A Roy Model With Multiple Markets," Working Papers 760, Princeton University, Department of Economics, Industrial Relations Section..
  6. Linton, Oliver & Whang, Yoon-Jae, 2002. "Nonparametric Estimation With Aggregated Data," Econometric Theory, Cambridge University Press, vol. 18(02), pages 420-468, April.
  7. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
  8. Camlong-Viot, Christine & Rodríguez-Póo, Juan M. & Vieu, Philippe, 2003. "Nonparametric and Semiparametric Estimation of Additive Models with both Discrete and Continuous Variables under Dependence," SFB 373 Discussion Papers 2003,38, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  9. Gozalo, Pedro L. & Linton, Oliver B., 2001. "Testing additivity in generalized nonparametric regression models with estimated parameters," Journal of Econometrics, Elsevier, Elsevier, vol. 104(1), pages 1-48, August.
  10. Donald, Stephen G., 1995. "Two-step estimation of heteroskedastic sample selection models," Journal of Econometrics, Elsevier, Elsevier, vol. 65(2), pages 347-380, February.
  11. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, Elsevier, vol. 79(1), pages 147-168, July.
  12. 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 for Research in Economics, Yale University.
  13. Das, M., 2003. "Identification and sequential estimation of panel data models with insufficient exclusion restrictions," Journal of Econometrics, Elsevier, Elsevier, vol. 114(2), pages 297-328, June.
  14. Li, Qi & Hsiao, Cheng & Zinn, Joel, 2003. "Consistent specification tests for semiparametric/nonparametric models based on series estimation methods," Journal of Econometrics, Elsevier, Elsevier, vol. 112(2), pages 295-325, February.
  15. Cai, Zongwu & Das, Mitali & Xiong, Huaiyu & Wu, Xizhi, 2006. "Functional coefficient instrumental variables models," Journal of Econometrics, Elsevier, Elsevier, vol. 133(1), pages 207-241, July.
  16. Jing Wang & Lijian Yang, 2009. "Efficient and fast spline-backfitted kernel smoothing of additive models," Annals of the Institute of Statistical Mathematics, Springer, Springer, vol. 61(3), pages 663-690, September.

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