This paper deals with the nonparametric estimation of P(X<Y) when both X and Y are observed with additional errors. We develop a deconvolution estimator and show that it is minimax optimal and adaptive in the case of supersmooth error distributions. Some numerical results are presented.

We consider the problem of estimating R=P(XY) where X and Y have independent exponential distributions with parameters θ and λ respectively and a common location parameter μ. Assuming that there is a prior guess or estimate R <Subscript>0</Subscript>, we develop various shrinkage estimators of R that incorporate...</subscript>