We introduce a nonparametric regression estimator that is consistent
in the presence of measurement error in the explanatory variable when
one repeated observation of the mismeasured regressor is available. The
approach taken relies on a useful property of the Fourier transform,
namely, its ability to convert complicated integral equations into
simple algebraic equations. The proposed estimator is shown to be
asymptotically normal, and its rate of convergence in probability is
derived as a function of the smoothness of the densities and
conditional expectations involved. The resulting rates are often
comparable to kernel deconvolution estimators, which provide consistent
estimation under the much stronger assumption that the density of the
measurement error is known. The finite-sample properties of the
estimator are investigated through Monte Carlo experiments.
Email your librarian or administrator to recommend adding this journal to your organisation's collection.
* Views captured on Cambridge Core between September 2016 - 23rd May 2017. This data will be updated every 24 hours.