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Theory of Probability and Mathematical Statistics

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Consistency of the least squares estimators of parameters in the texture surface sinusoidal model


Authors: A. V. Ivanov and O. V. Malyar
Translated by: S. V. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 97 (2017).
Journal: Theor. Probability and Math. Statist. 97 (2018), 73-84
MSC (2010): Primary 62J02; Secondary 62J99
DOI: https://doi.org/10.1090/tpms/1049
Published electronically: February 21, 2019
MathSciNet review: 3746000
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Abstract: We consider the texture surface sinusoidal model of observations. In other words, we consider a model where the regression function is the sum of two-parameter harmonic oscillations while the noise is an isotropic and homogeneous Gaussian random field on the plane. Conditions for the joint consistency of the least squares estimator of unknown amplitudes and angular frequencies are obtained for this trigonometric regression model.


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Additional Information

A. V. Ivanov
Affiliation: Department of Mathematical Analysis and Probability Theory, Faculty for Physics and Mathematics, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Peremogy Avenue, 37, Kyiv 03057, Ukraine
Email: alexntuu@gmail.com

O. V. Malyar
Affiliation: Department of Mathematical Analysis and Probability Theory, Faculty for Physics and Mathematics, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Peremogy Avenue, 37, Kyiv 03057, Ukraine
Email: malyar95@ukr.net

DOI: https://doi.org/10.1090/tpms/1049
Keywords: Texture surface sinusoidal model of observations, isotropic and homogeneous random field, least squares estimator, consistency
Received by editor(s): October 30, 2017
Published electronically: February 21, 2019
Article copyright: © Copyright 2019 American Mathematical Society