Two component binary statistical experiments with persistent linear regression
Author:
D. V. Koroliouk
Translated by:
S. Kvasko
Journal:
Theor. Probability and Math. Statist. 90 (2015), 103-114
MSC (2010):
Primary 60J70
DOI:
https://doi.org/10.1090/tpms/952
Published electronically:
August 7, 2015
MathSciNet review:
3242023
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: A sequence of binary statistical experiments generated by a sample of random variables with persistent linear regression is studied. A stochastic approximation for a sequence of statistical experiments is constructed in terms of an autoregressive process with normal noise. For a sequence of exponential statistical experiments, a stochastic approximation is constructed, as well, with the help of an exponential normal autoregressive process.
References
- D. V. Korolyuk, Recurrent statistical experiments with persistent linear regression, Ukr. Mat. Vesnik 10 (2013), no. 4, 497–506; English transl. in J. Math. Sci. 190 (2013), no. 4, 600–605.
- 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
- A. V. Skorokhod, Asimptoticheskie metody teorii stokhasticheskikh differentsial′nykh uravneniĭ, “Naukova Dumka”, Kiev, 1987 (Russian). MR 913305
- Yu. V. Borovskikh and V. S. Korolyuk, Martingale approximation, VSP, Utrecht, 1997. MR 1640099
- A. N. Shiryaev, Probability–2, MCNMO, Moscow, 2004. (Russian)
- Albert N. Shiryaev, Essentials of stochastic finance, Advanced Series on Statistical Science & Applied Probability, vol. 3, World Scientific Publishing Co., Inc., River Edge, NJ, 1999. Facts, models, theory; Translated from the Russian manuscript by N. Kruzhilin. MR 1695318
- Yu. S. Mishura and G. M. Shevchenko, Mathematics of Finance, Kyiv University Press, 2011. (Ukrainian)
- M. Abundo, L. Accardi, L. Stella, and N. Rosato, A stochastic model for the cooperative relaxation of proteins, based on a hierarchy of interactions between amino acidic residues, Math. Models Methods Appl. Sci. 8 (1998), no. 2, 327–358. MR 1618474, DOI https://doi.org/10.1142/S0218202598000147
- V. S. Korolyuk and D. Koroliuk, Diffusion approximation of stochastic Markov models with persistent regression, Ukraïn. Mat. Zh. 47 (1995), no. 7, 928–935 (English, with English and Ukrainian summaries); English transl., Ukrainian Math. J. 47 (1995), no. 7, 1065–1073 (1996). MR 1367948, DOI https://doi.org/10.1007/BF01084902
- A. Shcherbīna, Estimation of the mean in a model of a mixture with variable concentrations, Teor. Ĭmovīr. Mat. Stat. 84 (2011), 142–154 (Ukrainian, with English, Russian and Ukrainian summaries); English transl., Theory Probab. Math. Statist. 84 (2012), 151–164. MR 2857425, DOI https://doi.org/10.1090/S0094-9000-2012-00866-1
References
- D. V. Korolyuk, Recurrent statistical experiments with persistent linear regression, Ukr. Mat. Vesnik 10 (2013), no. 4, 497–506; English transl. in J. Math. Sci. 190 (2013), no. 4, 600–605.
- S. N. Ethier and T. G. Kurtz, Markov Processes: Characterization and Convergence, Wiley, New York, 1986. MR 838085 (88a:60130)
- A. V. Skorokhod, Asymptotic Methods in the Theory of Stochastic Differential Equations, “Naukova dumka”, Kiev, 1987; English transl., American Mathematical Society, Providence, RI, 2009. MR 913305 (88m:60164)
- Yu. V. Borovskikh and V. S. Korolyuk, Martingale Approximation, VSP, AH Zeist, 1997. MR 1640099 (99f:60001)
- A. N. Shiryaev, Probability–2, MCNMO, Moscow, 2004. (Russian)
- A. N. Shiryaev, Essentials of Stochastic Finance: Facts, Models, Theory “Fazis”, Moscow, 1998; English transl., World Scientific Pub. Co. Inc., Singapore, 1999. MR 1695318 (2000e:91085)
- Yu. S. Mishura and G. M. Shevchenko, Mathematics of Finance, Kyiv University Press, 2011. (Ukrainian)
- M. Abundo, L. Accardi, L. Stella, and N. Rosato, A stochastic model for the cooperative relaxation of proteins, based on a hierarchy of interactions between amino acidic residues, M3AS (Mathematical Models and Methods in Applied Sciences) 8 (1998), 327–358. MR 1618474 (99g:92020)
- V. S. Korolyuk and D. Koroliouk, Diffusion approximation of stochastic Markov models with persistent regression, Ukr. Math. J. 47 (1995), no. 7, 928–935. MR 1367948 (97j:60040)
- A. Shcherbina, Estimation of the mean value in a model of mixtures with varying concentrations, Teor. Imovirnost. Matem. Statyst. 84 (2011), 142–154; English transl. in Theor. Probability and Math. Statist. 84 (2012), 173–188. MR 2857425 (2012h:62130)
Similar Articles
Retrieve articles in Theory of Probability and Mathematical Statistics
with MSC (2010):
60J70
Retrieve articles in all journals
with MSC (2010):
60J70
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
Keywords:
Binary statistical experiment,
persistent linear regression,
stabilization,
stochastic approximation,
exponential statistical experiment,
exponential normal autoregressive process
Received by editor(s):
April 26, 2013
Published electronically:
August 7, 2015
Article copyright:
© Copyright 2015
American Mathematical Society
