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Minimax bounds for the risk function of estimators of functionals of
the spectral density of Gaussian
fields are obtained. This result is a generalization of a previous result of Khas'minskii and Ibragimov
on Gaussian processes.
Efficient estimators are then constructed for these functionals. In the case of linear functionals these estimators are
given for all dimensions. For non-linear integral functionals, these
estimators are constructed for the two and three dimensional problems.
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...
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...
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