The Annals of Statistics

Nonparametric regression with nonparametrically generated covariates

Enno Mammen, Christoph Rothe, and Melanie Schienle

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Abstract

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.

Article information

Source
Ann. Statist. Volume 40, Number 2 (2012), 1132-1170.

Dates
First available in Project Euclid: 18 July 2012

Permanent link to this document
https://projecteuclid.org/euclid.aos/1342625464

Digital Object Identifier
doi:10.1214/12-AOS995

Mathematical Reviews number (MathSciNet)
MR2985946

Zentralblatt MATH identifier
1274.62294

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

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

Citation

Mammen, Enno; Rothe, Christoph; Schienle, Melanie. Nonparametric regression with nonparametrically generated covariates. Ann. Statist. 40 (2012), no. 2, 1132--1170. doi:10.1214/12-AOS995. https://projecteuclid.org/euclid.aos/1342625464


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