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February 2006 Optimal change-point estimation from indirect observations
A. Goldenshluger, A. Tsybakov, A. Zeevi
Ann. Statist. 34(1): 350-372 (February 2006). DOI: 10.1214/009053605000000750

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.

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A. Goldenshluger. A. Tsybakov. A. Zeevi. "Optimal change-point estimation from indirect observations." Ann. Statist. 34 (1) 350 - 372, February 2006. https://doi.org/10.1214/009053605000000750

Information

Published: February 2006
First available in Project Euclid: 2 May 2006

zbMATH: 1091.62021
MathSciNet: MR2275245
Digital Object Identifier: 10.1214/009053605000000750

Subjects:
Primary: 62G05, 62G20

Rights: Copyright © 2006 Institute of Mathematical Statistics

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Vol.34 • No. 1 • February 2006
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