Nonparametric regression with nonparametrically generated covariates


Mammen, Enno ; Rothe, Christoph ; Schienle, Melanie


DOI: https://doi.org/10.1214/12-AOS995
URL: http://arxiv.org/pdf/1207.5594.pdf
Additional URL: http://projecteuclid.org/download/pdfview_1/euclid...
Document Type: Article
Year of publication: 2012
The title of a journal, publication series: The Annals of Statistics : An Official Journal of the Institute of Mathematical Statistics
Volume: 40
Issue number: 2
Page range: 1132-1170
Place of publication: Cleveland, Ohio [u.a.]
Publishing house: Inst. of Mathematical Statistics
ISSN: 0090-5364
Publication language: English
Institution: School of Law and Economics > Statistik (Mammen)
School of Law and Economics > Statistik (Rothe 2017-)
Außerfakultäre Einrichtungen > SFB 884
Außerfakultäre Einrichtungen > Graduate School of Economic and Social Sciences - CDSE (Economics)
Subject: 330 Economics
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.

Dieser Eintrag ist Teil der Universitätsbibliographie.




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Mammen, Enno ; Rothe, Christoph ; Schienle, Melanie (2012) Nonparametric regression with nonparametrically generated covariates. The Annals of Statistics : An Official Journal of the Institute of Mathematical Statistics Cleveland, Ohio [u.a.] 40 2 1132-1170 [Article]


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