Theory of Probability and Mathematical Statistics
Asymptotic properties of the periodogram estimates of the multivariate symmetric textured surface parameters
A. V. Ivanov, I. M. Savych and O. V. Dykyi
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Abstract: The simplest multivariate trigonometric model of symmetric textured surface is considered, that is observed on the background of homogeneous and isotropic Gaussian, in particular, strongly dependent random field on ℝM, M≥3. In the specified regression model strong consistency and asymptotic normality of periodogram estimates of amplitude and angular frequencies are proved.
Keywords: Multivariate trigonometric model, homogeneous and isotropic strongly dependent Gaussian random field, amplitude, angular frequencies, periodogram estimate, spectral measure of vector-function, strong consistency, asymptotic normality
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