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
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
MathSciNet review:
3241862
Full-text PDF Free Access
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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.
References
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- O. V. Īvanov and Ī. K. Matsak, Limit theorems for extremal residuals in linear and nonlinear regression models, Teor. Ĭmovīr. Mat. Stat. 86 (2011), 69–80 (Ukrainian, with English, Russian and Ukrainian summaries); English transl., Theory Probab. Math. Statist. 86 (2013), 79–91. MR 2986451, DOI https://doi.org/10.1090/S0094-9000-2013-00890-4
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References
- A. V. Ivanov, Asymptotic Theory of Nonlinear Regression, Kluwer Academic Publishers, Dordrecht–Boston–London, 1997. MR 1472234 (99h:62086)
- O. V. Ivanov and I. K. Matsak, Limit theorems for the maximal residuals in linear and nonlinear regression models, Teor. Imovirnost. Matem. Statyst. 86 (2012), 81–91; English transl. in Theor. Probability and Math. Statist. 86 (2013), 79–91. MR 2986451
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- I. I. Gihman and A. V. Skorohod, Introduction to the Theory of Random Processes, “Nauka”, Moscow, 1965; English transl., Saunders, Philadelphia, 1969. MR 0198534 (33:6689)
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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 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