A Journal "Theory of Probability and Mathematical Statistics"
2024
2023
2022
2021
2020
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   Special Issues   History  

Theory of Probability and Mathematical Statistics



A method for checking efficiency of estimators in statistical models driven by Lévy's noise

S. V. Bodnarchuk, D. O. Ivanenko

Download PDF

Abstract: A method for checking the efficiency of estimators of unknown parameters is proposed for statistical models with observations described by a stochastic differential equation driven by Lévy's noise.

Keywords: Asymptotic efficiency, local asymptotic normality, Lévy's processes, stochastic differential equations

Bibliography:
1. S. V. Bodnarchuk and A. M. Kulik, Stochastic control based on time-change transformations for stochastic processes with Lévy noise, Teor. Ĭmovir. Mat. Stat. 86 (2012), 11-27; English transl. in Theor. Probability and Math. Statist. 86 (2013), 13-31.
2. L. Chaumont and G. Uribe Bravo, Markovian bridges: Weak continuity and pathwise constructions, Ann. Probab. 39(2) (2011), 609-647.
3. J. Hájek, Local asymptotic minimax admissibility in estimation, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley-Los Angeles, 1971, pp. 175-194.
4. D. O. Ivanenko and A. M. Kulik, Malliavin calculus approach to statistical inference for Lévy driven SDE's, Methodol. Comput. Appl. Probab. (2013).
5. D. O. Ivanenko and A. M. Kulik, LAN property for discretely observed solutions to Lévy driven SDE's, Modern Stochastics: Theory and Appl. 1 (2014), 33-47.
6. A. M. Kulik, Exponential ergodicity of the solutions to SDE's with a jump noise, Stoch. Process. Appl. 119 (2009), no. 2, 602-632.
7. L. Le Cam, Limits of experiments, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley-Los Angeles, 1971, pp. 245-261.
8. L. Le Cam and G. L. Yang, Asymptotics in Statistics, Springer, Berlin-New York, 1990.
9. H. Masuda, Ergodicity and exponential β-mixing bounds for multidimensional diffusions with jumps, Stoch. Proc. Appl. 117 (2007), 35-56.
10. I. I. Gihman and A. V. Skorohod, Stochastic Differential Equations and their Applications, ''Naukova dumka'', Kiev, 1982. (Russian)
11. A. N. Shiryaev, Probability, MCNMO, Moscow, 2004; English transl. of the first Russian (1980) edition, Springer-Verlag, Berlin-Heidelberg-New York, 1996.