Work

Nonparametric estimation of an additive model with a link function

Year: 2004

Type: article

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.

Source: The Annals of Statistics

DOI: 10.1214/009053604000000814

Authors: Joel L. Horowitz, Enno Mammen

Institutions: Northwestern University, University of Mannheim

Language: English

Topic: Statistical Methods and Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Science Foundation, Alexander von Humboldt-Stiftung, Deutsche Forschungsgemeinschaft

Awards: Semiparametric and Nonparametric Methods in Econometrics, Nonparametric, Semiparametric, and Bootstrap Methods in Econometrics