Optimal change-point estimation from indirect observations

Details Optimal change-point estimation from indirect observations Optimal change-point estimation from indirect observations

2004-07-23

arxiv.org/abs/math/0407396v2

Annals of Statistics 2006, Vol. 34, No. 1, 350-372

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053605000000750 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053605000000750

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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