We estimate the anisotropic index of an anisotropic fractional brownian field. For all directions, we give a convergent estimator of the value of the anisotropic index in this direction, based on generalized quadratic variations. We also prove a central limit theorem. First we present a result of identification that relies on the asymptotic behavior of the spectral density of a process. Then, we define Radon transforms of the anisotropic fractional brownian field and prove that these processes admit a spectral density satisfying the previous assumptions. Finally we use simulated fields to test the proposed estimator in different anisotropic and isotropic cases. Results show that the estimator behaves similarly in all cases and is able to detect anisotropy quite accurately.
Classification : 60G60, 62M40, 60G15, 60G10, 60G17, 60G35, 44A12
Mots clés : anisotropic gaussian fields, identification, estimator, asymptotic normality, Radon transform
@article{PS_2008__12__30_0,
author = {Bierm\'e, Hermine and Richard, Fr\'ed\'eric},
title = {Estimation of anisotropic gaussian fields through {Radon} transform},
journal = {ESAIM: Probability and Statistics},
pages = {30--50},
publisher = {EDP-Sciences},
volume = {12},
year = {2008},
doi = {10.1051/ps:2007031},
mrnumber = {2367992},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps:2007031/}
}
TY - JOUR AU - Biermé, Hermine AU - Richard, Frédéric TI - Estimation of anisotropic gaussian fields through Radon transform JO - ESAIM: Probability and Statistics PY - 2008 DA - 2008/// SP - 30 EP - 50 VL - 12 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2007031/ UR - https://www.ams.org/mathscinet-getitem?mr=2367992 UR - https://doi.org/10.1051/ps:2007031 DO - 10.1051/ps:2007031 LA - en ID - PS_2008__12__30_0 ER -
Biermé, Hermine; Richard, Frédéric. Estimation of anisotropic gaussian fields through Radon transform. ESAIM: Probability and Statistics, Tome 12 (2008), pp. 30-50. doi : 10.1051/ps:2007031. http://www.numdam.org/articles/10.1051/ps:2007031/
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