Bandwidth selection for nonparametric regression with errors-in-variables

Abstract

We propose two novel bandwidth selection procedures for the nonparametric regression model with classical measurement error in the regressors. Each method evaluates the prediction errors of the regression using a second (density) deconvolution. The first approach uses a typical leave-one-out cross-validation criterion, while the second applies a bootstrap approach and the concept of out-of-bag prediction. We show the asymptotic validity of both procedures and compare them to the SIMEX method in a Monte Carlo study. As well as dramatically reducing computational cost, the methods proposed in this article lead to lower mean integrated squared error (MISE) compared to the current state-of-the-art.