A new nonparametric estimation procedure is introduced for the distribution function in a class of deconvolution problems, where the convolution density has one discontinuity. The estimator is shown to be consistent and its cube root asymptotic distribution theory is established. Known results on the minimax risk for the estimation problem indicate the estimator to be efficient.
"Isotonic inverse estimators for nonparametric deconvolution." Ann. Statist. 26 (6) 2395 - 2406, December 1998. https://doi.org/10.1214/aos/1024691476