Non parametric deconvolution of cumulative distribution function from repeated observations with unknown noise distribution

This article is devoted to the non parametric deconvolution problem of the cumulative distribution function from repeated observations with unknown noise distribution. The noise distribution is assumed to be symmetric around zero and can be consistently estimated from observed data without any additional data from that distribution. We suggest an estimator of the target function depending on a smoothing parameter and then study some asymptotic properties of the proposed estimator with respect to the pointwise mean squared error by assuming some regularity conditions on the target distribution as well as on the noise distribution. We also illustrate the effectiveness of our estimation via a simulation study.