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Theory of Probability and Mathematical Statistics



Asymptotic normality of the least squares estimator of two-dimensional sinusoidal observation model parameters

A. V. Ivanov, O. V. Lymar

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Abstract: In the paper the two-dimensional trigonometric observation model is considered. Various discrete modifications of such a sinusoidal model have received considerable attention in the literature on signal processing due to their application in the analysis of the textured surfaces. Under assumption that random noise is a homogeneous and isotropic Gaussian, in particular, strongly dependent random field on the plane, the asymptotic normality of the least squares estimator of this trigonometric regression model amplitudes and angular frequencies is proved.

Keywords: Two-dimensional sinusoidal model, homogeneous and isotropic Gaussian random field, least squares estimator, reduction theorem, asymptotic uniqueness, Brouwer fixed point theorem, spectral measure of regression function, μ-admissibility, asymptotic normality.

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