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Zbl 0983.62068
Ludeña, Carenne
Efficient estimation of functionals of the spectral density of stationary Gaussian fields. (English)
[J] ESAIM, Probab. Stat. 3, 23-47 (1999). ISSN 1292-8100; ISSN 1262-3318/e

Summary: 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 {\it R.Z. Khas'minskij} and {\it I.A. Ibragimov} [Probab. Theory Relat. Fields 73, 447-461 (1986; Zbl 0586.62057)] 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 nonlinear integral functionals, these estimators are constructed for two- and three-dimensional problems.

MSC 2000:: *62M40 Statistics of random fields
62M15 Spectral analysis of processes
62G05 Nonparametric estimation

Keywords: lower bounds; spectral density; Gaussian fields; linear functionals

Citations: Zbl 0586.62057; Zbl 0595.62037

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