Daisuke Kurisu and Taisuke Otsu

Published 19 July 2021

---

By utilizing intermediate Gaussian approximations, this paper establishes asymptotic linear representations of nonparametric deconvolution estimators for the classical measurement error model with repeated measurements. Our result is applied to derive confidence bands for the density and distribution functions of the error-free variable of interest and to establish faster convergence rates of the estimators than the ones obtained in the existing literature. Keywords: measurement error, deconvolution, asymptotic linear representation, intermediate Gaussian approximation, confidence band.