On linearization of nonparametric deconvolution estimators for repeated measurements model

Abstract

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. Due to slower decay rates of the linearization errors, however, our bootstrap counterparts for confidence bands need to be constructed by subsamples.