The Annals of Statistics

Nonparametric covariate-adjusted regression

Aurore Delaigle, Peter Hall, and Wen-Xin Zhou

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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.

Article information

Ann. Statist. Volume 44, Number 5 (2016), 2190-2220.

Received: May 2015
Revised: November 2015
First available in Project Euclid: 12 September 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation 62G08: Nonparametric regression 62G20: Asymptotic properties

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


Delaigle, Aurore; Hall, Peter; Zhou, Wen-Xin. Nonparametric covariate-adjusted regression. Ann. Statist. 44 (2016), no. 5, 2190--2220. doi:10.1214/16-AOS1442.

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Supplemental materials

  • Supplement to “Nonparametric covariate-adjusted regression”. This supplemental material contains more details for the implementation of the proposed estimators, additional simulation results as well as additional proofs omitted in the main text.