Heteroscedastic Deconvolution of $${{\mathbb {P}}(X<Y)}$$ with Compactly Supported Error Densities

Abstract

We deal with the problem of the nonparametric estimation of $${\mathbb {P}}\left( {X < Y} \right)$$ which is also known as the stress–strength model problem when both X and Y are observed with additional errors. We provide the convergence rate for the suggested estimator and give a lower bound in the case that the error random variables have different distributions. Some numerical results are also presented.