Open Access
April 2012 Nonparametric regression with nonparametrically generated covariates
Enno Mammen, Christoph Rothe, Melanie Schienle
Ann. Statist. 40(2): 1132-1170 (April 2012). DOI: 10.1214/12-AOS995


We analyze the statistical properties of nonparametric regression estimators using covariates which are not directly observable, but have be estimated from data in a preliminary step. These so-called generated covariates appear in numerous applications, including two-stage nonparametric regression, estimation of simultaneous equation models or censored regression models. Yet so far there seems to be no general theory for their impact on the final estimator’s statistical properties. Our paper provides such results. We derive a stochastic expansion that characterizes the influence of the generation step on the final estimator, and use it to derive rates of consistency and asymptotic distributions accounting for the presence of generated covariates.


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Enno Mammen. Christoph Rothe. Melanie Schienle. "Nonparametric regression with nonparametrically generated covariates." Ann. Statist. 40 (2) 1132 - 1170, April 2012.


Published: April 2012
First available in Project Euclid: 18 July 2012

zbMATH: 1274.62294
MathSciNet: MR2985946
Digital Object Identifier: 10.1214/12-AOS995

Primary: 62G08 , 62G20

Keywords: empirical process , Nonparametric regression , simultaneous equation models , two-stage estimators

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 2 • April 2012
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