On the distribution of the clipping median under a mixture model

Motivated by applications in image processing, quality control, and econometrics we derive the exact distribution function of the clipping median estimator which is designed to provide simultaneously robust smooth and jump-preserving reconstructions. We allow for a mixture model which is of special interest for applications in pixel-wise object detection. To construct statistical tests for pixel classification, we propose to rely on estimated p-values. Simulations suggest that the resulting approximations are reliable.