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.
Mots-clés : local asymptotic normality, lacunar wavelet series
@article{PS_2011__15__69_0, author = {Loubes, Jean-Michel and Paindaveine, Davy}, title = {Local {Asymptotic} {Normality} {Property} for {Lacunar} {Wavelet} {Series} multifractal model}, journal = {ESAIM: Probability and Statistics}, pages = {69--82}, publisher = {EDP-Sciences}, volume = {15}, year = {2011}, doi = {10.1051/ps/2009005}, mrnumber = {2870506}, zbl = {1270.60045}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ps/2009005/} }
TY - JOUR AU - Loubes, Jean-Michel AU - Paindaveine, Davy TI - Local Asymptotic Normality Property for Lacunar Wavelet Series multifractal model JO - ESAIM: Probability and Statistics PY - 2011 SP - 69 EP - 82 VL - 15 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2009005/ DO - 10.1051/ps/2009005 LA - en ID - PS_2011__15__69_0 ER -
%0 Journal Article %A Loubes, Jean-Michel %A Paindaveine, Davy %T Local Asymptotic Normality Property for Lacunar Wavelet Series multifractal model %J ESAIM: Probability and Statistics %D 2011 %P 69-82 %V 15 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2009005/ %R 10.1051/ps/2009005 %G en %F PS_2011__15__69_0
Loubes, Jean-Michel; Paindaveine, Davy. Local Asymptotic Normality Property for Lacunar Wavelet Series multifractal model. ESAIM: Probability and Statistics, Tome 15 (2011), pp. 69-82. doi : 10.1051/ps/2009005. http://www.numdam.org/articles/10.1051/ps/2009005/
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