Convergence Rates of Multivariate Regression Estimators with Errors-In-Variables

This paper studies the regression estimation with errors-in-variables. We first extend Meister’s theorems (Meister, 2009. Deconvolution Problems in Nonparametric Statistics. Springer, Berlin) from one to multi-dimensional setting, when a noise density has no zeros in the Fourier domain. Then motivated by the work of Delaigle and Meister (Delaigle, Meister, 2011. Nonparametric function estimation under Fourier-oscillating noise. Statistica Sinica 21, 1065–1092), we show a desired convergence rate of a kernel estimator for Fourier-oscillating noises. Finally, two technical conditions are removed, when a wavelet estimator is used.