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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 ofthe spectral density of Gaussianfields 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 aregiven for all dimensions. For non-linear integral functionals, theseestimators 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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