Change-point estimation from indirect observations. 1. Minimax complexity
The subject of this paper is the problem of nonparametric estimation of signal singularities form indirect and noisy observations. Here by singularity we mean a discontinuity (change--point) of the signal or of its derivative. The model of indirect observations we consider is that of a linear transform of the signal, observed in white noise. The estimation problem is analyzed in a minimax framework. We provide lower bounds for minimax risks and propose rate-optimal estimation procedures.