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Theory of Probability and Mathematical Statistics

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Binary statistical experiments with persistent nonlinear regression


Author: D. V. Koroliouk
Translated by: V. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 91 (2014).
Journal: Theor. Probability and Math. Statist. 91 (2015), 71-80
MSC (2010): Primary 62F05, 60J70, 62M05
DOI: https://doi.org/10.1090/tpms/967
Published electronically: February 3, 2016
MathSciNet review: 3364124
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Abstract: A sequence of binary stochastic experiments with persistent nonlinear regression is considered. The regression is defined as a product of a linear directed force and nonlinear term changing the directed force in a neighborhood of boundary points. A stochastic approximation for the sequence of stationary experiments is constructed with the help of an autoregressive process with normal perturbation. A stochastic approximation of the sequence of exponential stochastic experiments is also constructed with the help of an exponential autoregressive process.


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Additional Information

D. V. Koroliouk
Affiliation: Institute of Telecommunications and Global Information Space of National Academy of Science of Ukraine, Chokolovskiĭ Blvd., 13, Kyiv, 03110, Ukraine
Email: dimitri.koroliouk@ukr.net

DOI: https://doi.org/10.1090/tpms/967
Keywords: Binary statistical experiment, persistent regression, equilibrium state, stochastic approximation, exponential stochastic experiment, exponential normal autoregressive process
Received by editor(s): April 26, 2013
Published electronically: February 3, 2016
Article copyright: © Copyright 2016 American Mathematical Society