NONPARAMETRIC COVARIATE-ADJUSTED REGRESSION
Aurore Delaigle, Peter Hall, Wen-Xin Zhou
The Annals of Statistics | INST MATHEMATICAL STATISTICS | Published : 2016
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 e..View full abstract
Supported by grants and fellowships from the Australian Research Council.