Consistency of LSE for the many-dimensional symmetric textured surface parameters

Abstract

A multivariate trigonometric regression model is considered. In the paper strong consistency of the least squares estimator for amplitudes and angular frequencies is obtained for such a multivariate model on the assumption that the random noise is a homogeneous or homogeneous and isotropic Gaussian, specifically, strongly dependent random field on ${\mathbb{R}^{M}},M\ge 3$.

Keywords

• Multivariate trigonometric model
• homogeneous and isotropic strongly dependent Gaussian random field
• least squares estimate in the Walker–Brillinger sense
• strong consistency