Optimal change-point estimation from indirect observations
摘要
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.
引用
@article{arxiv.math/0407396,
title = {Optimal change-point estimation from indirect observations},
author = {A. Goldenshluger and A. Tsybakov and A. Zeevi},
journal= {arXiv preprint arXiv:math/0407396},
year = {2007}
}
备注
Published at http://dx.doi.org/10.1214/009053605000000750 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)