Change-point estimation from indirect observations. 2. Adaptation
We focus on the problem of adaptive estimation of signal singularities from indirect and noisy observations. A typical example of such singularity we can be a discontinuity (change--point) of the signal or of its derivative. We develop a change--point estimator which adapts to unknown smoothness of a nuisance deterministic component and to unknown jump amplitude. We show that the proposed estimator attains optimal adaptive rates of convergence. A simulation study demonstrates a reasonable practical behavior of the proposed adaptive estimates.