We consider the problem of nonparametric estimation of signal singularities from 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.
Publié le : 2008-10-15
Classification:
Change-point estimations,
Ill-posed problems,
Minimax risk,
Sequence space model,
Optimal rates of convergence,
62G05,
62G20
@article{1222261913,
author = {Goldenshluger, A. and Juditsky, A. and Tsybakov, A. B. and Zeevi, A.},
title = {Change-point estimation from indirect observations. 1. Minimax complexity},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {44},
number = {2},
year = {2008},
pages = { 787-818},
language = {en},
url = {http://dml.mathdoc.fr/item/1222261913}
}
Goldenshluger, A.; Juditsky, A.; Tsybakov, A. B.; Zeevi, A. Change-point estimation from indirect observations. 1. Minimax complexity. Ann. Inst. H. Poincaré Probab. Statist., Tome 44 (2008) no. 2, pp. 787-818. http://gdmltest.u-ga.fr/item/1222261913/