The Annals of Statistics

Optimal change-point estimation from indirect observations

A. Goldenshluger, A. Tsybakov, and A. Zeevi

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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.

Article information

Ann. Statist., Volume 34, Number 1 (2006), 350-372.

First available in Project Euclid: 2 May 2006

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Zentralblatt MATH identifier

Primary: 62G05: Estimation 62G20: Asymptotic properties

Change-point estimation deconvolution minimax risk ill-posedness probe functional optimal rates of convergence


Goldenshluger, A.; Tsybakov, A.; Zeevi, A. Optimal change-point estimation from indirect observations. Ann. Statist. 34 (2006), no. 1, 350--372. doi:10.1214/009053605000000750.

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