Estimation of anisotropic Gaussian fields through Radon transform

Hermine Biermé; Frédéric Richard

ESAIM: Probability and Statistics (2007)

  • Volume: 12, page 30-50
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Biermé, Hermine, and Richard, Frédéric. "Estimation of anisotropic Gaussian fields through Radon transform." ESAIM: Probability and Statistics 12 (2007): 30-50. <http://eudml.org/doc/104402>.

@article{Biermé2007,
abstract = { 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. },
author = {Biermé, Hermine, Richard, Frédéric},
journal = {ESAIM: Probability and Statistics},
keywords = {Anisotropic Gaussian fields; identification; estimator; asymptotic normality; Radon transform.; anisotropic Gaussian fields; Radon transform},
language = {eng},
month = {11},
pages = {30-50},
publisher = {EDP Sciences},
title = {Estimation of anisotropic Gaussian fields through Radon transform},
url = {http://eudml.org/doc/104402},
volume = {12},
year = {2007},
}

TY - JOUR
AU - Biermé, Hermine
AU - Richard, Frédéric
TI - Estimation of anisotropic Gaussian fields through Radon transform
JO - ESAIM: Probability and Statistics
DA - 2007/11//
PB - EDP Sciences
VL - 12
SP - 30
EP - 50
AB - 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.
LA - eng
KW - Anisotropic Gaussian fields; identification; estimator; asymptotic normality; Radon transform.; anisotropic Gaussian fields; Radon transform
UR - http://eudml.org/doc/104402
ER -

References

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