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.

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Alexander Goldenshluger, A. Tsybakov, and Assaf Zeevi
Journal Article
Publication Date
The Annals of Statistics

Full Citation

Goldenshluger, Alexander, A. Tsybakov, and Assaf Zeevi
. “Optimal change-point estimation from indirect observations.”
The Annals of Statistics
, (February 01, 2006):