Optimality properties in estimating jumps

Abstract : We study the problem of optimal estimation of the jumps for stochastic processes. We assume that the stochastic process is discretely observed with a sampling step of size 1/n. We first propose an estimator of the sequence of jumps based on the discrete observations. This estimator has rate sqrt(n) and we give an explicit expression for its asymptotic error. Next, we show some lower bounds for the estimation of the jumps. When the marks of the underlying jump component are deterministic, we prove a LAMN property. We deduce then some convolution theorem, in the case where the marks of the jump component are random. Especially, this implies the optimality of our estimator.
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Pré-publication, Document de travail
2011
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https://hal.archives-ouvertes.fr/hal-00609983
Contributeur : Emmanuelle Clément <>
Soumis le : mercredi 20 juillet 2011 - 15:59:01
Dernière modification le : vendredi 10 février 2017 - 01:12:30
Document(s) archivé(s) le : lundi 12 novembre 2012 - 11:20:55

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LAMN_estim_19juillet.pdf
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  • HAL Id : hal-00609983, version 1

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Emmanuelle Clement, Sylvain Delattre, Arnaud Gloter. Optimality properties in estimating jumps. 2011. <hal-00609983>

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