Local Asymptotic Normality Property for Lacunar Wavelet Series multifractal model

Jean-Michel Loubes; Davy Paindaveine

ESAIM: Probability and Statistics (2011)

  • Volume: 15, page 69-82
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Loubes, Jean-Michel, and Paindaveine, Davy. "Local Asymptotic Normality Property for Lacunar Wavelet Series multifractal model." ESAIM: Probability and Statistics 15 (2011): 69-82. <http://eudml.org/doc/277147>.

@article{Loubes2011,
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.},
author = {Loubes, Jean-Michel, Paindaveine, Davy},
journal = {ESAIM: Probability and Statistics},
keywords = {local asymptotic normality; lacunar wavelet series},
language = {eng},
pages = {69-82},
publisher = {EDP-Sciences},
title = {Local Asymptotic Normality Property for Lacunar Wavelet Series multifractal model},
url = {http://eudml.org/doc/277147},
volume = {15},
year = {2011},
}

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
PB - EDP-Sciences
VL - 15
SP - 69
EP - 82
AB - 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.
LA - eng
KW - local asymptotic normality; lacunar wavelet series
UR - http://eudml.org/doc/277147
ER -

References

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