B-spline estimation of regression functions with errors in variable

This paper proposes a new B-spline method for nonparametric regression function estimation which can be applied to the case even when the covariate is contaminated with noise. A property of B-splines, reproducing line property, is crucial in the construction of B-spline estimators for regression function. To account for errors in covariate, deconvolution is involved in the construction of B-spline estimators. It is shown that the B-spline estimators achieve the optimal rate of convergence which depends on the tail behavior of the characteristic function of the error distribution.