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
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
MathSciNet review:
3364123
Full-text PDF Free Access
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Additional Information
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.
References
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References
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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
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
