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

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

Annales de l'I.H.P. Probabilités et statistiques (2008)

  • Volume: 44, Issue: 5, page 787-818
  • ISSN: 0246-0203

Abstract

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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.

How to cite

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Goldenshluger, A., et al. "Change-point estimation from indirect observations. 1. Minimax complexity." Annales de l'I.H.P. Probabilités et statistiques 44.5 (2008): 787-818. <http://eudml.org/doc/77992>.

@article{Goldenshluger2008,
abstract = {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.},
author = {Goldenshluger, A., Juditsky, A., Tsybakov, A. B., Zeevi, A.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {change-point estimations; ill-posed problems; minimax risk; sequence space model; optimal rates of convergence},
language = {eng},
number = {5},
pages = {787-818},
publisher = {Gauthier-Villars},
title = {Change-point estimation from indirect observations. 1. Minimax complexity},
url = {http://eudml.org/doc/77992},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Goldenshluger, A.
AU - Juditsky, A.
AU - Tsybakov, A. B.
AU - Zeevi, A.
TI - Change-point estimation from indirect observations. 1. Minimax complexity
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2008
PB - Gauthier-Villars
VL - 44
IS - 5
SP - 787
EP - 818
AB - 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.
LA - eng
KW - change-point estimations; ill-posed problems; minimax risk; sequence space model; optimal rates of convergence
UR - http://eudml.org/doc/77992
ER -

References

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