Nonparametric covariate-adjusted regression

TL;DR

This paper develops nonparametric methods for estimating regression curves under multiplicative distortion caused by confounding variables, offering flexible estimators with strong theoretical properties and good empirical performance.

Contribution

It introduces a range of estimators for covariate-adjusted regression under multiplicative distortion, including a novel piecewise approach applicable in general scenarios.

Findings

Estimators share asymptotic properties with ideal estimators using undistorted data.

Methods perform well on simulated datasets.

Methods demonstrate good performance on real datasets.

Abstract

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.