We study nonparametric change-point estimation from indirect noisy observations. Focusing on the white noise convolution model, we consider two classes of functions that are smooth apart from the change-point. We establish lower bounds on the minimax risk in estimating the change-point and develop rate optimal estimation procedures. The results demonstrate that the best achievable rates of convergence are determined both by smoothness of the function away from the change-point and by the degree of ill-posedness of the convolution operator. Optimality is obtained by introducing a new technique that involves, as a key element, detection of zero crossings of an estimate of the properly smoothed second derivative of the underlying function.
Publié le : 2006-02-14
Classification:
Change-point estimation,
deconvolution,
minimax risk,
ill-posedness,
probe functional,
optimal rates of convergence,
62G05,
62G20
@article{1146576266,
author = {Goldenshluger, A. and Tsybakov, A. and Zeevi, A.},
title = {Optimal change-point estimation from indirect observations},
journal = {Ann. Statist.},
volume = {34},
number = {1},
year = {2006},
pages = { 350-372},
language = {en},
url = {http://dml.mathdoc.fr/item/1146576266}
}
Goldenshluger, A.; Tsybakov, A.; Zeevi, A. Optimal change-point estimation from indirect observations. Ann. Statist., Tome 34 (2006) no. 1, pp. 350-372. http://gdmltest.u-ga.fr/item/1146576266/