Abstract
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.
Original language | English |
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Pages (from-to) | 350-372 |
Number of pages | 23 |
Journal | Annals of Statistics |
Volume | 34 |
Issue number | 1 |
DOIs | |
State | Published - Feb 2006 |
Keywords
- Change-point estimation
- Deconvolution
- Ill-posedness
- Minimax risk
- Optimal rates of convergence
- Probe functional
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty