Annals of Statistics

Nonparametric estimation of an additive model with a link function

Joel L. Horowitz and Enno Mammen

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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 estimator has an oracle property. The asymptotic distribution of each additive component is the same as it would be if the other components were known with certainty.

Article information

Ann. Statist., Volume 32, Number 6 (2004), 2412-2443.

First available in Project Euclid: 7 February 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G08: Nonparametric regression
Secondary: 62G20: Asymptotic properties

Additive models multivariate curve estimation nonparametric regression kernel estimates orthogonal series estimator


Horowitz, Joel L.; Mammen, Enno. Nonparametric estimation of an additive model with a link function. Ann. Statist. 32 (2004), no. 6, 2412--2443. doi:10.1214/009053604000000814.

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