Nonparametric estimation of an additive model with a link function
Joel L. Horowitz and Enno Mammen
Source: Ann. Statist. Volume 32, Number 6
(2004), 2412-2443.
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 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.
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Keywords: Additive models; multivariate curve estimation; nonparametric regression; kernel estimates; orthogonal series estimator
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aos/1107794874
Digital Object Identifier: doi:10.1214/009053604000000814
Mathematical Reviews number (MathSciNet): MR2153990
Zentralblatt MATH identifier: 1069.62035
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