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Nonparametric estimation of an additive model with a link function


  • Horowitz, Joel L.
  • Mammen, Enno


This paper describes an estimator of the additive components of a nonparametric additive model with a known link function. When the additive components are twice continuously differentiable, the estimator is asymptotically normally distributed with a rate of convergence in probability of n -2/5 . This is true regardless of the (finite) dimension of the explanatory variable. Thus, in contrast to the existing asymptotically normal estimator, the new estimator has no curse of dimensionality. Moreover, the asymptotic distribution of each additive component is the same as it would be if the other components were known with certainty.

Suggested Citation

  • Horowitz, Joel L. & Mammen, Enno, 2002. "Nonparametric estimation of an additive model with a link function," SFB 373 Discussion Papers 2002,63, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  • Handle: RePEc:zbw:sfb373:200263

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    References listed on IDEAS

    1. Oliver Linton & E. Mammen & J. Nielsen, 1997. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions," Cowles Foundation Discussion Papers 1160, Cowles Foundation for Research in Economics, Yale University.
    2. Opsomer, Jean D., 2000. "Asymptotic Properties of Backfitting Estimators," Journal of Multivariate Analysis, Elsevier, vol. 73(2), pages 166-179, May.
    3. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
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    Cited by:

    1. Arthur Lewbel & Oliver Linton, 2003. "Nonparametric Estimation of Homothetic and Homothetically Separable Functions," STICERD - Econometrics Paper Series 461, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. Oliver Linton & Enno Mammen, 2003. "Estimating Semiparametric ARCH (8) Models by Kernel Smoothing Methods," STICERD - Econometrics Paper Series 453, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. O. Linton & E. Mammen, 2005. "Estimating Semiparametric ARCH(∞) Models by Kernel Smoothing Methods," Econometrica, Econometric Society, vol. 73(3), pages 771-836, May.
    4. Horowitz, Joel L. & Lee, Sokbae, 2005. "Nonparametric Estimation of an Additive Quantile Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1238-1249, December.
    5. Arthur Lewbel & Oliver Linton, 2007. "Nonparametric Matching and Efficient Estimators of Homothetically Separable Functions," Econometrica, Econometric Society, vol. 75(4), pages 1209-1227, July.


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