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

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

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)787-818
Number of pages32
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume44
Issue number5
DOIs
StatePublished - Oct 2008
Externally publishedYes

Keywords

  • Change-point estimations
  • Ill-posed problems
  • Minimax risk
  • Optimal rates of convergence
  • Sequence space model

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