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Nonparametric estimation of an additive model with a link function

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  • Horowitz, Joel L.
  • Mammen, Enno
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    Abstract

    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. --

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    File URL: http://econstor.eu/bitstream/10419/65347/1/727039741.pdf
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    Bibliographic Info

    Paper provided by Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes in its series SFB 373 Discussion Papers with number 2002,63.

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    Date of creation: 2002
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    Handle: RePEc:zbw:sfb373:200263

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    Related research

    Keywords: nonparametric regression; additive models; multivariate curve estimation; kernel estimates; orthogonal series estimator;

    References

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    1. Oliver Linton & Enno Mammen & N Nielsen, 2000. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm under Weak Conditions," STICERD - Econometrics Paper Series /2000/386, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    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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    Citations

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    Cited by:
    1. 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.
    2. Enno Mammen & Oliver Linton, 2004. "Estimating Semiparametric ARCH Models by Kernel Smoothing Methods," FMG Discussion Papers dp511, Financial Markets Group.
    3. Arthur Lewbel & Oliver Linton, 2003. "Nonparametric Estimation of Homothetic and Homothetically Separable Functions," STICERD - Econometrics Paper Series /2003/461, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    4. Arthur Lewbel & Oliver Linton, 2007. "Nonparametric Matching and Efficient Estimators of Homothetically Separable Functions," Econometrica, Econometric Society, vol. 75(4), pages 1209-1227, 07.

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