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October 2016 Nonparametric covariate-adjusted regression
Aurore Delaigle, Peter Hall, Wen-Xin Zhou
Ann. Statist. 44(5): 2190-2220 (October 2016). DOI: 10.1214/16-AOS1442


We consider nonparametric estimation of a regression curve when the data are observed with multiplicative distortion which depends on an observed confounding variable. We suggest several estimators, ranging from a relatively simple one that relies on restrictive assumptions usually made in the literature, to a sophisticated piecewise approach that involves reconstructing a smooth curve from an estimator of a constant multiple of its absolute value, and which can be applied in much more general scenarios. We show that, although our nonparametric estimators are constructed from predictors of the unobserved undistorted data, they have the same first-order asymptotic properties as the standard estimators that could be computed if the undistorted data were available. We illustrate the good numerical performance of our methods on both simulated and real datasets.


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Aurore Delaigle. Peter Hall. Wen-Xin Zhou. "Nonparametric covariate-adjusted regression." Ann. Statist. 44 (5) 2190 - 2220, October 2016.


Received: 1 May 2015; Revised: 1 November 2015; Published: October 2016
First available in Project Euclid: 12 September 2016

zbMATH: 1349.62097
MathSciNet: MR3546448
Digital Object Identifier: 10.1214/16-AOS1442

Primary: 62G05 , 62G08 , 62G20

Keywords: Discontinuities , local linear estimator , multiplicative distortion , Nadaraya–Watson estimator , nonparametric smoothing , predictors

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.44 • No. 5 • October 2016
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