Testing Gaussianity and linearity for random fields in the frequency domain (Q2740048)
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scientific article; zbMATH DE number 1646469
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Testing Gaussianity and linearity for random fields in the frequency domain |
scientific article; zbMATH DE number 1646469 |
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16 September 2001
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bispectrum
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kernel smoothed estimator
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asymptotic normality
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Testing Gaussianity and linearity for random fields in the frequency domain (English)
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For a stationary random field on \(R^d\) the theory of normalized bispectrum estimation is described. A theorem of asymptotic normality of kernel-smoothed \(k\)-th order periodogram estimates of the normalized bispectrum is demonstrated. It is used to derive an (asymptotic) log likelihood ratio statistic for the test of Gaussianity (more precisely, of the hypothesis that the k-th order spectrum is identically zero) and for the test of linearity (the k-th order spectrum is a constant).
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