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.

Visit the Annales de l'Institut Henri Poincaré 

Authors
Alexander Goldenshluger, A. Juditsky, A. Tsybakov, and Assaf Zeevi
Format
Journal Article
Publication Date
Journal
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Full Citation

Goldenshluger, Alexander, A. Juditsky, A. Tsybakov, and Assaf Zeevi
. “Change-point estimation from indirect observations. 1. Minimax complexity.”
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
vol.
44
, (January 01, 2008):
787
-
818
.