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.
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Goldenshluger, Alexander, A. Juditsky, A. Tsybakov, and Assaf Zeevi. "Change-point estimation from indirect observations. 1. Minimax complexity." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 44, no. 5 (2008): 787-818.
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