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Nonparametric estimation of an additive model with a link function

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  • Joel L. Horowitz
  • Enno Mammen

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.

Suggested Citation

  • Joel L. Horowitz & Enno Mammen, 2002. "Nonparametric estimation of an additive model with a link function," CeMMAP working papers 19/02, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:19/02
    DOI: 10.1920/wp.cem.2002.1902
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    References listed on IDEAS

    as
    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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