Estimation of nonparametric regression models with a mixture of Berkson and classical errors

We consider the estimation of nonparametric regression models with the explanatory variable being measured with Berkson errors or with a mixture of Berkson and classical errors. By constructing a compact operator, the regression function is the solution of an ill-posed inverse problem, and we propose an estimation procedure based on Tikhonov regularization. Under mild conditions, the convergence rate of proposed estimator is derived. The finite-sample properties of the estimator are investigated through simulation studies.