Oracle-efficient nonparametric estimation of an additive model with an unknown link function

Joel L. Horowitz, Enno Mammen

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


This paper describes an estimator of the additive components of a nonparametric additive model with an unknown link function. When the additive components and link function are twice differentiable with sufficiently smooth second derivatives, 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, the estimator has no curse of dimensionality. Moreover, the asymptotic distribution of the estimator of each additive component is the same as it would be if the link function and the other components were known with certainty. Thus, asymptotically there is no penalty for not knowing the link function or the other components.

Original languageEnglish (US)
Pages (from-to)582-608
Number of pages27
JournalEconometric Theory
Issue number3
StatePublished - Jun 1 2011

ASJC Scopus subject areas

  • Social Sciences (miscellaneous)
  • Economics and Econometrics


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