Change-point estimation from indirect observations. 2. Adaptation

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

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

  • Volume: 44, Issue: 5, page 819-836
  • ISSN: 0246-0203

Abstract

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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 behavior of the proposed adaptive estimates.

How to cite

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Goldenshluger, A., et al. "Change-point estimation from indirect observations. 2. Adaptation." Annales de l'I.H.P. Probabilités et statistiques 44.5 (2008): 819-836. <http://eudml.org/doc/77993>.

@article{Goldenshluger2008,
abstract = {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 behavior of the proposed adaptive estimates.},
author = {Goldenshluger, A., Juditsky, A., Tsybakov, A., Zeevi, A.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {singularities; change-point; estimation; detection; minimax risk; adaption; optimal rates},
language = {eng},
number = {5},
pages = {819-836},
publisher = {Gauthier-Villars},
title = {Change-point estimation from indirect observations. 2. Adaptation},
url = {http://eudml.org/doc/77993},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Goldenshluger, A.
AU - Juditsky, A.
AU - Tsybakov, A.
AU - Zeevi, A.
TI - Change-point estimation from indirect observations. 2. Adaptation
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2008
PB - Gauthier-Villars
VL - 44
IS - 5
SP - 819
EP - 836
AB - 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 behavior of the proposed adaptive estimates.
LA - eng
KW - singularities; change-point; estimation; detection; minimax risk; adaption; optimal rates
UR - http://eudml.org/doc/77993
ER -

References

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  1. [1] L. Brown and M. Low. A constrained risk inequality with applications to nonparametric functional estimation. Ann. Statist. 24 (1996) 2524–2535. Zbl0867.62023MR1425965
  2. [2] A. Goldenshluger, A. Juditsky, A. Tsybakov and A. Zeevi. Change-point estimation from indirect observations. 1. Minimax complexity. Ann. Inst. Henri Poincaré 44 (2008) 787–818. Zbl1206.62048MR2453845
  3. [3] O. V. Lepskii. A problem of adaptive estimation in Gaussian white noise. Theory Probab. Appl. 35 (1990) 454–466. Zbl0725.62075MR1091202
  4. [4] O. V. Lepskii and V. Spokoiny. Optimal pointwise adaptive methods in nonparametric estimation. Ann. Statist. 25 (1997) 2512–2546. Zbl0894.62041MR1604408
  5. [5] A. Zygmund. Trigonometric Series, Vol. I, 2nd edition. Cambridge Univ. Press, 1959. Zbl0085.05601MR107776

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