Theory of Probability and Mathematical Statistics
On the least squares estimator asymptotic normality of the multivariate symmetric textured surface parameters
A. V. Ivanov, I. M. Savych
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Abstract: A multivariate trigonometric regression model is considered. Various discrete modifications of the similar bivariate model received serious attention in the literature on signal and image processing due to multiple applications in the analysis of symmetric textured surfaces. In the paper asymptotic normality of the least squares estimator for amplitudes and angular frequencies is obtained in multivariate trigonometric model assuming that the random noise is a homogeneous or homogeneous and isotropic Gaussian, in particular, strongly dependent random field on $\mathbb{R}^M,\,\, M>2.$
Keywords: Multivariate trigonometric model, texture surface, homogeneous and isotropic Gaussian random field, covariance function, spectral density, least squares estimate in the Walker sense, linearization theorem, asymptotic uniqueness, spectral measure of regression function, Brouwer fixed-point theorem, $\mu$-admissibility, asymptotic normality
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