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H 1 Large scale reduction simple

Auteurs : Clausel, Marianne (Auteur de la Conférence)
CIRM (Editeur )

Résumé : Consider a non-linear function $G(X_t)$ where $X_t$ is a stationary Gaussian sequence with long-range dependence. The usual reduction principle states that the partial sums of $G(X_t)$ behave asymptotically like the partial sums of the first term in the expansion of $G$ in Hermite polynomials. In the context of the wavelet estimation of the long-range dependence parameter, one replaces the partial sums of $G(X_t)$ by the wavelet scalogram, namely the partial sum of squares of the wavelet coefficients. Is there a reduction principle in the wavelet setting, namely is the asymptotic behavior of the scalogram for $G(X_t)$ the same as that for the first term in the expansion of $G$ in Hermite polynomial? The answer is negative in general. This paper provides a minimal growth condition on the scales of the wavelet coefficients which ensures that the reduction principle also holds for the scalogram. The results are applied to testing the hypothesis that the long-range dependence parameter takes a specific value. Joint work with François Roueff and Murad S. Taqqu

Keywords: long-range dependence; long memory; self-similarity; wavelet transform; estimation; hypothesis
testing

Codes MSC :
42C40 - Wavelets and other special systems
60G18 - Self-similar processes
60G20 - Generalized stochastic processes
62M15 - Spectral analysis of processes
60G22 - Fractional processes, including fractional Brownian motion

 Informations sur la Vidéo Langue : Anglais Date de publication : 01/03/16 Date de captation : 18/02/16 Collection : Research talks ; Probability and Statistics Format : MP4 Durée : 00:32:34 Domaine : Probability & Statistics Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2016-02-18_Clausel.mp4 Informations sur la rencontre Nom de la rencontre : Thematic month on statistics - Week 3: Processus / Mois thématique sur les statistiques - Semaine 3 : ProcessusOrganisateurs de la rencontre : Boutahar, Mohamed ; Reboul, LaurenceDates : 15/02/16 - 19/02/16 Année de la rencontre : 2016 URL Congrès : http://conferences.cirm-math.fr/1617.htmlCitation Data DOI : 10.24350/CIRM.V.18931903 Cite this video as: Clausel, Marianne (2016). Large scale reduction simple. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18931903 URI : http://dx.doi.org/10.24350/CIRM.V.18931903

### Voir aussi

Bibliographie

1. Clausel, M., Roueff, F., & Taqqu, M. (2014). Large scale reduction principle and application to hypothesis testing. - http://arxiv.org/abs/1407.5871

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