2019
2018
2017
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
1977
1976
1975
1974
1973
1972
1971
1970


Archive

About   Editorial Board   Contacts   Template   Publication Ethics   Peer Review Process

Theory of Probability and Mathematical Statistics
(Teoriya Imovirnostei ta Matematychna Statystyka)



Two component binary statistical experiments with persistent linear regression

D. V. Koroliouk

Download PDF

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.

Keywords: Binary statistical experiment, persistent linear regression, stabilization, stochastic approximation, exponential statistical experiment, exponential normal autoregressive process

Bibliography:
1. 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.
2. S. N. Ethier and T. G. Kurtz, Markov Processes: Characterization and Convergence, Wiley, New York, 1986.
3. A. V. Skorokhod, Asymptotic Methods in the Theory of Stochastic Differential Equations, ''Naukova dumka'', Kiev, 1987; English transl., American Mathematical Society, Providence, RI, 2009.
4. Yu. V. Borovskikh and V. S. Korolyuk, Martingale Approximation, VSP, AH Zeist, 1997.
5. A. N. Shiryaev, Probability-2, MCNMO, Moscow, 2004. (Russian)
6. A. N. Shiryaev, Essentials of Stochastic Finance: Facts, Models, Theory ''Fazis'', Moscow, 1998; English transl., World Scientific Pub. Co. Inc., Singapore, 1999.
7. Yu. S. Mishura and G. M. Shevchenko, Mathematics of Finance, Kyiv University Press, 2011. (Ukrainian)
8. 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.
9. V. S. Korolyuk and D. Koroliouk, Diffusion approximation of stochastic Markov models with persistent regression, Ukr. Math. J. 47 (1995), no. 7, 928-935.
10. 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.