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Efficient estimation of functionals of the spectraldensity of stationary Gaussian fields

Published online by Cambridge University Press:  15 August 2002

Carenne Ludeña
Carenne Ludeña*
Affiliation:
Departamento de Matemáticas, IVIC, Caracas, Venezuela; cludena@ivic.ivic.ve.
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Abstract

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.

Keywords

Efficient estimationGaussian fieldsperiodogramtapered periodogramspectral densityToeplitz matrices.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 3 , 1999 , pp. 23 - 47
Copyright
© EDP Sciences, SMAI, 1999

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