Smooth Backfitting in Errors-in-Variables Additive Models

Abstract

We study nonparametric additive regression models when noisy covariates are observed within measurement errors. Based on deconvolution techniques, we construct an iterative algorithm for smooth backfitting of additive function in the presence of errors-in-variables. We show that the smooth backfitting achieves univariate accuracy of the standard deconvolution for estimating each component function under certain conditions. Deconvolving noise on backfitting is confined into negligible magnitude that rate of convergence of the proposed estimator is accelerated when the smoothness of measurement errors falls into a certain range. We also present finite sample performance of the deconvolution smooth backfitting in comparison with a naive application of the standard smooth backfitting ignoring measurement errors. Monte Carlo simulation is demonstrated that our method gives smaller mean integrated squared errors than the naive one in average.