Deconvolution of cumulative distribution function from repeated measurements with uniform noises

Abstract

This work is devoted to the estimation of a cumulative distribution function (CDF) using repeated measurements contaminated by additive noise. The noise is assumed to follow a uniform distribution on [−S,S] with an unknown S>0. Since the characteristic function of the noise exhibits real periodic zeros, the estimation strategies in the existing literature cannot be applied directly. We introduce an estimator for the CDF involving two tuning parameters, constructed using the ridge regularization method. The consistency of the estimator with respect to the mean squared error is established under certain conditions on these parameters. Furthermore, an error estimate is derived assuming the target distribution possesses finite smoothness. A simulation study is performed to evaluate the finite-sample performances of the proposed estimator. An application to a real dataset is also presented.