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Stochastic asymptotic expansion of correlogram estimator of the correlation function of random noise in nonlinear regression model


Authors: O. V. Ivanov and K. K. Moskvichova
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 90 (2014).
Journal: Theor. Probability and Math. Statist. 90 (2015), 87-101
MSC (2010): Primary 60G50, 65B10, 60G15; Secondary 40A05
DOI: https://doi.org/10.1090/tpms/951
Published electronically: August 6, 2015
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Abstract: A correlogram estimator of the covariance function of a stationary Gaussian noise is considered in a nonlinear regression model with continuous time. The estimator is constructed from deviations of the observed stochastic process from the regression function where the least squares estimator is substituted for the unknown parameter. A stochastic asymptotic expansion of the correlogram estimator of the covariance function is obtained for the case where the time of observations tends to infinity.


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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/951
Keywords: Nonlinear regression model with continuous time, stationary Gaussian noise, covariance function, least squares estimator, stochastic asymptotic expansion
Received by editor(s): July 31, 2013
Published electronically: August 6, 2015
Article copyright: © Copyright 2015 American Mathematical Society