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.

The Hough transform is a common computer vision algorithm used to detect shapes in a noisy image. Originally the Hough transform was proposed as a technique for detection of straight lines in images. In this paper we study the statistical properties of the Hough transform estimator in the...