We focus on the problem of adaptive estimation of signal singularities from indirect and noisy observations. A typical example of such a singularity is a discontinuity (change-point) of the signal or of its derivative. We develop a change-point estimator which adapts to the unknown smoothness of a nuisance deterministic component and to an unknown jump amplitude. We show that the proposed estimator attains optimal adaptive rates of convergence. A simulation study demonstrates reasonable practical behavior of the proposed adaptive estimates.
@article{1222261914,
author = {Goldenshluger, A. and Juditsky, A. and Tsybakov, A. and Zeevi, A.},
title = {Change-point estimation from indirect observations. 2. Adaptation},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {44},
number = {2},
year = {2008},
pages = { 819-836},
language = {en},
url = {http://dml.mathdoc.fr/item/1222261914}
}
Goldenshluger, A.; Juditsky, A.; Tsybakov, A.; Zeevi, A. Change-point estimation from indirect observations. 2. Adaptation. Ann. Inst. H. Poincaré Probab. Statist., Tome 44 (2008) no. 2, pp. 819-836. http://gdmltest.u-ga.fr/item/1222261914/