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Change-point estimation from indirect observations. 1. Minimax complexity

A. Goldenshluger;  A. Juditsky;  A. B. Tsybakov;  A. Zeevi — 2008

Annales de l'I.H.P. Probabilités et statistiques

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.

Change-point estimation from indirect observations. 2. Adaptation

A. Goldenshluger;  A. Juditsky;  A. Tsybakov;  A. Zeevi — 2008

Annales de l'I.H.P. Probabilités et statistiques

We focus on the problem of adaptive estimation of signal singularities from indirect and noisy observations. A typical example of such a singularity is a discontinuity (change-point) of the signal or of its derivative. We develop a change-point estimator which adapts to the unknown smoothness of a nuisance deterministic component and to an unknown jump amplitude. We show that the proposed estimator attains optimal adaptive rates of convergence. A simulation study demonstrates reasonable practical...

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