Abstract
Background. For sinusoidal observation model of textured surface, i.e. model where regression function is a two-parameter harmonic oscillation and noise is a homogeneous isotropic Gaussian random field on the plane with zero mean and covariance function of the special kind, the problem of statistical estimation of sinusoidal model unknown amplitudes and angular frequencies is considered.Objective. The aim of the paper is to study asymptotic behavior of the least squares estimate (LSE) of unknown amplitudes and angular frequencies of textured surface sinusoidal model.Methods. The results were obtained on the application of methodology developed in the papers by A.V. Ivanov et al. (2009, 2015) and monograph by A.V. Ivanov, N.N. Leonenko (1989).Results. Sufficient conditions on random noise covariance function that ensure strong consistency of sinusoidal model parameters LSE are obtained.Conclusions. The obtained results allow extending them on the models where regression function is a sum of several two-parameter harmonic oscillations. Besides LSE consistency property will allow proving asymptotic normality of these estimates in further works.
Highlights
For sinusoidal observation model of textured surface, i.e. model where regression function is a two-parameter harmonic oscillation and noise is a homogeneous isotropic Gaussian random field on the plane with zero mean and covariance function of the special kind, the problem of statistical estimation of sinusoidal model unknown amplitudes and angular frequencies is considered
The results were obtained on the application of methodology developed in the papers
The obtained results allow extending them on the models where regression function is a sum of several two-parameter harmonic oscillations
Summary
For sinusoidal observation model of textured surface, i.e. model where regression function is a two-parameter harmonic oscillation and noise is a homogeneous isotropic Gaussian random field on the plane with zero mean and covariance function of the special kind, the problem of statistical estimation of sinusoidal model unknown amplitudes and angular frequencies is considered. The aim of the paper is to study asymptotic behavior of the least squares estimate (LSE) of unknown amplitudes and angular frequencies of textured surface sinusoidal model. Sufficient conditions on random noise covariance function that ensure strong consistency of sinusoidal model parameters LSE are obtained. The obtained results allow extending them on the models where regression function is a sum of several two-parameter harmonic oscillations. Besides LSE consistency property will allow proving asymptotic normality of these estimates in further works
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Research Bulletin of the National Technical University of Ukraine "Kyiv Politechnic Institute"
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
