Efficient estimation of functionals of the spectral density of stationary Gaussian fields

Free access article

Issue		ESAIM: PS Volume 3, 1999


Page(s)		23 - 47
DOI		10.1051/ps:1999101

DOI: 10.1051/ps:1999101

ESAIM: PS, June 1999, Vol. 3, p. 23-47

Efficient estimation of functionals of the spectral density of stationary Gaussian fields

Estimation efficace de fonctionnelles de la densité spectrale des champs Gaussiens stationnaires

Carenne Ludeña
Departamento de Matemáticas, IVIC, Caracas, Venezuela (cludena@ivic.ivic.ve)

Received June 7, 1996. Revised September 17, 1998.

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.

Résumé: Nous considérons le problème d'estimation d'une fonctionnelle de la densité spectrale d'un champ gaussien. Nous établissons tout d'abord des bornes inférieures asymptotiques pour le risque minimax. Dans le cas des champs de dimension 2 ou 3, nous construisons ensuite des estimateurs efficaces, c'est à dire atteignant asymptotiquement ces bornes inférieures, pour des fonctionnelles linéaires et des fonctionnelles intégrales non linéaires de la densité spectrale.

Keywords and phrases: Efficient estimation, Gaussian fields, periodogram, tapered periodogram, spectral density, Toeplitz matrices.

AMS Subject Classification: 62G05, 62M40, 62M15.

Article without figures.

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