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Asymptotic normality of the correlogram estimator of the covariance function of a random noise in the nonlinear regression model


Authors: O. V. Ivanov and K. K. Moskvichova
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 91 (2014).
Journal: Theor. Probability and Math. Statist. 91 (2015), 61-70
MSC (2010): Primary 60G50, 65B10, 60G15; Secondary 40A05
DOI: https://doi.org/10.1090/tpms/966
Published electronically: February 3, 2016
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Abstract: The asymptotic behavior of the correlogram estimator of the covariance function of a random noise is studied for the nonlinear regression model. A functional theorem on the asymptotic normality of the estimator is proved in the space of continuous functions.


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Additional Information

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

K. K. Moskvichova
Affiliation: Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine “Kiev Polytechnic Institute”, Peremogy Avenue, 37, Kyiv 03056, Ukraine
Email: kamok@ua.fm

DOI: https://doi.org/10.1090/tpms/966
Keywords: Nonlinear regression model, stationary Gaussian process, covariance function, spectral density, correlogram estimator, random element, convergence in distribution, asymptotic normality
Received by editor(s): August 20, 2014
Published electronically: February 3, 2016
Article copyright: © Copyright 2016 American Mathematical Society