Optimal change-point estimation from indirect observations

By Alexander Goldenshluger, Alexandre B. Tsybakov, Assaf J. Zeevi. 2004

53 citations recorded by the source corpus.

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.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4420dd249c824e980b0041c55d4a7b90c71eff53

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Citations in the corpus

Detecting gradual changes in locally stationary processes (2013, methodology): “Raimondo (1998) and Goldenshluger et al. (2006) who derive minimax rates in the model with Gaussian errors].”