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Asymptotic properties of Ibragimov's estimator for a parameter of the spectral density of the random noise in a nonlinear regression model


Authors: A. V. Ivanov and V. V. Prikhod’ko
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 93 (2015).
Journal: Theor. Probability and Math. Statist. 93 (2016), 51-70
MSC (2010): Primary 60G50, 65B10, 60G15; Secondary 40A05
DOI: https://doi.org/10.1090/tpms/1003
Published electronically: February 7, 2017
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Abstract: A nonlinear regression model with continuous time is considered. The consistency and asymptotic normality of the Ibragimov estimator for a parameter of the spectral density of the Gaussian stationary noise are obtained.


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Additional Information

A. V. Ivanov
Affiliation: Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine “KPI”, Peremogy Avenue, 37, Kyiv 03056, Ukraine
Email: alexntuu@gmail.com

V. V. Prikhod’ko
Affiliation: Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine “KPI”, Peremogy Avenue, 37, Kyiv 03056, Ukraine
Email: vikaprihodko@ukr.net

DOI: https://doi.org/10.1090/tpms/1003
Keywords: Nonlinear regression model with continuous time, Gaussian stationary noise, residual periodogram, Ibragimov's estimator of a spectral density, consistency, asymptotic normality
Received by editor(s): August 25, 2015
Published electronically: February 7, 2017
Additional Notes: This paper was prepared following the talk at the International conference “Probability, Reliability and Stochastic Optimization (PRESTO-2015)” held in Kyiv, Ukraine, April 7–10, 2015
Article copyright: © Copyright 2017 American Mathematical Society