Nonparametric covariate-adjusted regression. (English) Zbl 1349.62097

Delaigle, Aurore; Hall, Peter; Zhou, Wen-Xin

Ann. Stat. 44, No. 5, 2190-2220 (2016).

Summary: 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.

MSC:

62G05	Nonparametric estimation
62G08	Nonparametric regression and quantile regression
62G20	Asymptotic properties of nonparametric inference

Keywords:

discontinuities; local linear estimator; multiplicative distortion; Nadaraya-Watson estimator; nonparametric smoothing; predictors