Optimal change-point estimation from indirect observations

A. Goldenshluger, A. Tsybakov, A. Zeevi

Research output: Contribution to journalArticlepeer-review

Abstract

We study nonparametric change-point estimation from indirect noisy observations. Focusing on the white noise convolution model, we consider two classes of functions that are smooth apart from the change-point. We establish lower bounds on the minimax risk in estimating the change-point and develop rate optimal estimation procedures. The results demonstrate that the best achievable rates of convergence are determined both by smoothness of the function away from the change-point and by the degree of ill-posedness of the convolution operator. Optimality is obtained by introducing a new technique that involves, as a key element, detection of zero crossings of an estimate of the properly smoothed second derivative of the underlying function.

Original languageEnglish
Pages (from-to)350-372
Number of pages23
JournalAnnals of Statistics
Volume34
Issue number1
DOIs
StatePublished - Feb 2006
Externally publishedYes

Keywords

  • Change-point estimation
  • Deconvolution
  • Ill-posedness
  • Minimax risk
  • Optimal rates of convergence
  • Probe functional

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