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Asymptotic properties of $ M$-estimators of parameters of a nonlinear regression model with a random noise whose spectrum is singular


Authors: A. V. Ivanov and I. V. Orlovskyi
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 93 (2015).
Journal: Theor. Probability and Math. Statist. 93 (2016), 33-49
MSC (2010): Primary 62J02; Secondary 62J99
DOI: https://doi.org/10.1090/tpms/993
Published electronically: February 7, 2017
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Abstract: Time continuous nonlinear regression model with a noise being a nonlinearly transformed Gaussian stationary process with a singular spectrum is considered in the paper. Sufficient conditions for the asymptotic normality of the $ M$-estimator are found for the vector parameter in this model.


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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

I. V. Orlovskyi
Affiliation: Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine “KPI”, Peremogy Avenue, 37, Kyiv 03056, Ukraine
Email: i.v.orlovsky@gmail.com

DOI: https://doi.org/10.1090/tpms/993
Keywords: Asymptotic uniqueness of an estimator, asymptotic normality, $M$-estimators, nonlinear regression models, singular spectrum
Received by editor(s): August 5, 2015
Published electronically: February 7, 2017
Additional Notes: The 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