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Nonparametric estimation of an additive model with a link function

  • Joel Horowitz


    (Institute for Fiscal Studies and Northwestern University)

  • Enno Mammen


    (Institute for Fiscal Studies and University of Mannheim)

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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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP19/02.

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Length: 34 pp.
Date of creation: Jul 2002
Date of revision:
Handle: RePEc:ifs:cemmap:19/02
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  1. Opsomer, Jean D., 2000. "Asymptotic Properties of Backfitting Estimators," Journal of Multivariate Analysis, Elsevier, vol. 73(2), pages 166-179, May.
  2. repec:cep:stiecm:/2000/386 is not listed on IDEAS
  3. Enno Mammen & Oliver Linton & J Nielsen, 2000. "The existence and asymptotic properties of a backfitting projection algorithm under weak conditions," LSE Research Online Documents on Economics 2315, London School of Economics and Political Science, LSE Library.
  4. 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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