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Local Asymptotic Normality Property for Lacunar Wavelet Series multifractal model*

Published online by Cambridge University Press:  05 January 2012

Jean-Michel Loubes  and
Davy Paindaveine
Jean-Michel Loubes
Affiliation:
Institut de Mathématique de Toulouse, France; jean-michel.loubes@math.univ-toulouse.fr
Davy Paindaveine
Affiliation:
Université Libre de Bruxelles, Belgium.
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Abstract

We consider a lacunar wavelet series function observed with an additive Brownian motion. Such functions are statistically characterized by two parameters. The first parameter governs the lacunarity of the wavelet coefficients while the second one governs its intensity. In this paper, we establish the local and asymptotic normality (LAN) of the model, with respect to this couple of parameters. This enables to prove the optimality of an estimator for the lacunarity parameter, and to build optimal (in the Le Cam sense) tests on the intensity parameter.

Keywords

Local asymptotic normalitylacunar wavelet series
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 15: Supplement: In honor of Marc Yor , 2011 , pp. 69 - 82
Copyright
© EDP Sciences, SMAI, 2011

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