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Theory of Probability and Mathematical Statistics
(Teoriya Imovirnostei ta Matematychna Statystyka)



Consistency of the least squares estimator of the textured surface sinusoidal model parameters

A. V. Ivanov, O. V. Maliar

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Abstract: For sinusoidal observation model of textured surface, i. e. for model where regression function is a sum of two-parameter harmonic oscillations and noise is a homogeneous isotropic Gaussian random field on the plane, the strong consistency conditions of unknown amplitudes and angular frequencies least squares estimates of indicated trigonometric regression model are obtained.

Keywords: Sinusoidal model of textured surface, homogeneous isotropic random field, least squares estimates, consistency

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