Change-point estimation from indirect observations. 2. Adaptation

A. Goldenshluger, A. Juditsky, A. Tsybakov, A. Zeevi

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)819-836
Number of pages18
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume44
Issue number5
DOIs
StatePublished - Oct 2008

Keywords

  • Adaption
  • Change-point
  • Detection
  • Estimation
  • Minimax risk
  • Optimal rates
  • Singularities

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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