Semiparametric density estimation of shifts between curves

In this paper we address a problem related to curve alignment with a semiparametric framework, that is without any knowledge of the shape. This problem appears in many biological applications, in which we are interested in the estimation of the elapsed duration distribution between two signals, but wish to estimate it with a possibly low signal-noise ratio, and without any knowledge of the pulse shape, since it varies from one framework to another. Following recent advances in period estimation in a semiparametric setting, we suggest an estimator based on a smooth functional of the periodogram. We present results on simulations for a neuroscience issue, as well as on real data for the alignment of ECG signals; both show the usefulness of the method, as well as its robustness to the noise level.

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