Multivariate statistical experiments with persistent non-linear regression and equilibrium
Author:
D. V. Koroliouk
Translated by:
N. Semenov
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
MathSciNet review:
3553427
Full-text PDF Free Access
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Additional Information
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
- D. V. Koroliouk, Binary repeating statistical experiments with persistent linear regression, Ukr. Matem. Vestnik 10 (2013), no. 4, 497–506. (Russian)
- 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, DOI 10.1090/tpms/952
- M. B. Nevel′son and R. Z. Has′minskiĭ, Stochastic approximation and recursive estimation, Translations of Mathematical Monographs, Vol. 47, American Mathematical Society, Providence, R.I., 1973. Translated from the Russian by the Israel Program for Scientific Translations. MR 0423714
- 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, DOI 10.1090/S0094-9000-2015-00943-1
- 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, DOI 10.1002/9780470316658
- Yu. V. Borovskikh and V. S. Korolyuk, Martingale approximation, VSP, Utrecht, 1997. MR 1640099
References
- D. V. Koroliouk, Binary repeating statistical experiments with persistent linear regression, Ukr. Matem. Vestnik 10 (2013), no. 4, 497–506. (Russian)
- D. V. Koroliouk, Two component binary statistical experiments with persistent linear regression, Teor. Ĭmovir. Mat. Stat. 90 (2014), 91–101; English transl. in Theor. Probability and Math. Statist. 90 (2015), 103–114. MR 3242023
- M. B. Nevel’son and R. Z. Has’minskiĭ, Stochastic Approximation and Recursive Estimation, “Nauka”, Moscow, 1972; English transl., American Mathematical Society, Providence, 1973. MR 0423714
- D. S. Pupashenko, S. V. Shklyar, and A. G. Kukush, Asymptotic properties of corrected score estimator in autoregressive model with measurement errors, Teor. Ĭmovir. Mat. Stat. 89 (2013), 156–166; English transl. in Theory Probab. Math. Statist. 89 (2014), 169–180. MR 3235183
- Stewart N. Ethier and Thomas G. Kurtz, Markov Processes: Characterization and Convergence, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons, Inc., New York, 1986. MR 838085
- Yu. V. Borovskikh and V. S. Koroliyuk, 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
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
