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Multivariate statistical experiments with persistent non-linear regression and equilibrium


Author: D. V. Koroliouk
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 92 (2015).
Journal: Theor. Probability and Math. Statist. 92 (2016), 71-79
MSC (2010): Primary 62F05, 60J70, 62M05
DOI: https://doi.org/10.1090/tpms/983
Published electronically: August 10, 2016
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Abstract: A sequence of multivariate statistical experiments with persistent non-linear regression is considered. This sequence is determined by a matrix of directing actions for frequencies of certain attributes. Conditions for the convergence of multivariate statistical experiments to a state of equilibrium are studied. A stochastic approximation by an autoregressive process with normal perturbations is constructed for the discrete time model.


References [Enhancements On Off] (What's this?)

  • 1. D. V. Koroliouk, Binary repeating statistical experiments with persistent linear regression, Ukr. Matem. Vestnik 10 (2013), no. 4, 497-506. (Russian)
  • 2. D. V. Korolyuk, Two-component binary statistical experiments with persistent linear regression, Teor. Ĭmovīr. Mat. Stat. 90 (2014), 91–101 (Ukrainian, with English, Russian and Ukrainian summaries); English transl., Theory Probab. Math. Statist. 90 (2015), 103–114. MR 3242023
  • 3. M. B. Nevel′son and R. Z. Has′minskiĭ, Stochastic approximation and recursive estimation, American Mathematical Society, Providence, R. I., 1973. Translated from the Russian by the Israel Program for Scientific Translations; Translations of Mathematical Monographs, Vol. 47. MR 0423714
  • 4. D. S. Pupashenko, S. V. Shklyar, and A. G. Kukush, Asymptotic properties of corrected score estimator in autoregressive model with measurement errors, Teor. Ĭmovīr. Mat. Stat. 89 (2013), 156–166 (English, with English, Russian and Ukrainian summaries); English transl., Theory Probab. Math. Statist. 89 (2014), 169–180. MR 3235183, https://doi.org/10.1090/S0094-9000-2015-00943-1
  • 5. Stewart N. Ethier and Thomas G. Kurtz, Markov processes, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons, Inc., New York, 1986. Characterization and convergence. MR 838085
  • 6. Yu. V. Borovskikh and V. S. Korolyuk, Martingale approximation, VSP, Utrecht, 1997. MR 1640099

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Additional Information

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

DOI: https://doi.org/10.1090/tpms/983
Keywords: Multivariate statistical experiments, regression function, equilibrium, stochastic approximation
Received by editor(s): September 22, 2014
Published electronically: August 10, 2016
Article copyright: © Copyright 2016 American Mathematical Society