Change-point estimation from indirect observations. 1. Minimax complexity
A. Goldenshluger, A. Juditsky, A. Tsybakov and A. Zeevi
Ann. Inst. H. Poincare Probab. Statist. Volume 44, Number 5, pp. 787-818, 2008.

Abstract

The subject of this paper is the problem of nonparametric estimation of signal singularities form 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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