# Semi-parametric estimation of shifts

Abstract : We observe a large number of functions differing from each other only by a translation parameter. While the main pattern is unknown, we propose to estimate the shift parameters using $M$-estimators. Fourier transform enables to transform this statistical problem into a semi-parametric framework. We study the convergence of the estimator and provide its asymptotic behavior. Moreover, we use the method in the applied case of velocity curve forecasting.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-00347905
Contributor : Jean-Michel Loubes <>
Submitted on : Wednesday, December 17, 2008 - 9:54:10 AM
Last modification on : Friday, April 12, 2019 - 4:22:49 PM

### Identifiers

• HAL Id : hal-00347905, version 1
• ARXIV : 0712.1936

### Citation

Fabrice Gamboa, Jean-Michel Loubes, Elie Maza. Semi-parametric estimation of shifts. 2007. ⟨hal-00347905⟩

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