| Issue |
ESAIM: PS
Volume 15, 2011
|
|
|---|---|---|
| Page(s) | 69 - 82 | |
| DOI | https://doi.org/10.1051/ps/2009005 | |
| Published online | 05 January 2012 | |
Local Asymptotic Normality Property for Lacunar Wavelet Series multifractal model*
1
Institut de Mathématique de Toulouse, France; jean-michel.loubes@math.univ-toulouse.fr
2
Université Libre de Bruxelles, Belgium.
Received:
8
October
2008
Revised:
25
March
2009
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.
Mathematics Subject Classification: 60G17 / 62G07
Key words: Local asymptotic normality / lacunar wavelet series
© EDP Sciences, SMAI, 2011
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