IDEAS home Printed from https://ideas.repec.org/a/cup/etheor/v6y1990i04p466-479_00.html
   My bibliography  Save this article

Additive Interactive Regression Models: Circumvention of the Curse of Dimensionality

Author

Listed:
  • 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.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 that AIR models do circumvent the curse of dimensionality. A lower bound on the rate of convergence 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.

Suggested Citation

  • Andrews, Donald W.K. & Whang, Yoon-Jae, 1990. "Additive Interactive Regression Models: Circumvention of the Curse of Dimensionality," Econometric Theory, Cambridge University Press, vol. 6(4), pages 466-479, December.
    • Handle: RePEc:cup:etheor:v:6:y:1990:i:04:p:466-479_00
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S0266466600005478/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Andrews, Donald W K, 1991. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Econometrica, Econometric Society, vol. 59(2), pages 307-345, 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, vol. 15(2), pages 211-245, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. V. Chernozhukov & I. Fernández-Val & A. Galichon, 2009. "Improving point and interval estimators of monotone functions by rearrangement," Biometrika, Biometrika Trust, vol. 96(3), pages 559-575.
    2. Ann , Jihee & Park, Cheolbeom, 2022. "Demographic Structure and House Prices in the United States: Reconciliation Using Metropolitan Area Data," Journal of Economic Development, The Economic Research Institute, Chung-Ang University, vol. 47(3), pages 57-71, September.
    3. Donald, Stephen G., 1995. "Two-step estimation of heteroskedastic sample selection models," Journal of Econometrics, Elsevier, vol. 65(2), pages 347-380, February.
    4. Gao, Jiti & Tong, Howell & Wolff, Rodney, 2002. "Model Specification Tests in Nonparametric Stochastic Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 324-359, November.
    5. Mark Jensen, 1997. "Revisiting the flexibility and regularity properties of the asymptotically ideal production model," Econometric Reviews, Taylor & Francis Journals, vol. 16(2), pages 179-203.
    6. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    7. Hujer Reinhard & Grammig Joachim & Kokot Stefan, 2000. "Time Varying Trade Intensities and the Deutsche Telekom IPO / Zeitvariable Handelsintensitaten und die Deutsche Telekom IPO," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 220(6), pages 689-714, December.
    8. Ai, Chunrong & McFadden, Daniel, 1997. "Estimation of some partially specified nonlinear models," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 1-37.
    9. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    10. Barnett, William A. & Serletis, Apostolos, 2008. "Consumer preferences and demand systems," Journal of Econometrics, Elsevier, vol. 147(2), pages 210-224, December.
    11. Marco Gallegati, 2019. "A system for dating long wave phases in economic development," Journal of Evolutionary Economics, Springer, vol. 29(3), pages 803-822, July.
    12. Ichimura, Hidehiko & Todd, Petra E., 2007. "Implementing Nonparametric and Semiparametric Estimators," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 74, Elsevier.
    13. Yue-Jun Zhang & Han Zhang, 2023. "Volatility Forecasting of Crude Oil Market: Which Structural Change Based GARCH Models have Better Performance?," The Energy Journal, , vol. 44(1), pages 175-194, January.
    14. Kari Harju & Syed Mujahid Hussain, 2011. "Intraday Seasonalities and Macroeconomic News Announcements," European Financial Management, European Financial Management Association, vol. 17(2), pages 367-390, March.
    15. Li, Qi, 1996. "On the root-N-consistent semiparametric estimation of partially linear models," Economics Letters, Elsevier, vol. 51(3), pages 277-285, June.
    16. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
    17. Mohsen Bahmani-Oskooee & Tsangyao Chang & Zahra (Mila) Elmi & Omid Ranjbar, 2018. "Re-testing Prebisch–Singer hypothesis: new evidence using Fourier quantile unit root test," Applied Economics, Taylor & Francis Journals, vol. 50(4), pages 441-454, January.
    18. Barnett, William A. & Serletis, Apostolos, 2008. "The Differential Approach to Demand Analysis and the Rotterdam Model," MPRA Paper 12319, University Library of Munich, Germany.
    19. Williams, Jonathan, 2004. "Determining management behaviour in European banking," Journal of Banking & Finance, Elsevier, vol. 28(10), pages 2427-2460, October.
    20. Fleissig, Adrian & Swofford, James L., 1996. "A dynamic asymptotically ideal model of money demand," Journal of Monetary Economics, Elsevier, vol. 37(2-3), pages 371-380, April.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cup:etheor:v:6:y:1990:i:04:p:466-479_00. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Kirk Stebbing (email available below). General contact details of provider: https://www.cambridge.org/ect .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.