EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 24 (2020) ESAIM: PS, 24 (2020) 827-841 References
Open Access
Issue
ESAIM: PS
Volume 24, 2020
Page(s) 827 - 841
DOI https://doi.org/10.1051/ps/2020022
Published online 24 November 2020
  1. A. Aït-Sahalia and J. Jacod, Fisher’s information for discretely sampled Lévy processes. Econometrica 76 (2008) 727–761. [CrossRef] [MathSciNet] [Google Scholar]
  2. C. Berzin and J. Léon, Estimation in models driven by fractional Brownian motion. Ann. Inst. Henri Poincaré - Probab. Statist. 44 (2008) 191–213. [CrossRef] [Google Scholar]
  3. A. Brouste and M. Fukasawa, Local asymptotic normality property for fractional Gaussian noise under high-frequency observations. Ann. Statist. 46 (2018) 2045–2061. [CrossRef] [Google Scholar]
  4. A. Brouste and H. Masuda, Efficient estimation of stable Lévy process with symmetric jumps. Statist. Inference Stoch. Processes 21 (2018) 289–307. [CrossRef] [Google Scholar]
  5. J.F. Cœurjolly, Simulation and identification of the fractional Brownian motion: a bibliographical and comparative study. J. Statist. Softw. 5 (2000) 1–53. [Google Scholar]
  6. S. Cohen, F. Gamboa, C. Lacaux and J.-M. Loubes, LAN property for some fractional type Brownian motion. ALEA: Latin Am. J. Probab. Math. Statist. 10 (2013) 91–106. [Google Scholar]
  7. R. Dahlhaus, Efficient parameter estimation for self-similar processes. Ann. Statist. 17 (1989) 1749–1766. [CrossRef] [MathSciNet] [Google Scholar]
  8. R. Dahlhaus, Correction efficient parameter estimation for self-similar processes. Ann. Statist. 34 (2006) 1045–1047. [CrossRef] [Google Scholar]
  9. P. Flandrin, Wavelet analysis and synthesis of fractional Brownian motion. IEEE Trans. Inform. Theory 38 (1992) 910–917. [CrossRef] [MathSciNet] [Google Scholar]
  10. R. Fox and M. Taqqu, Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series. Ann. Statist. 14 (1986) 517–532. [CrossRef] [MathSciNet] [Google Scholar]
  11. M. Fukasawa and T. Takabatake, Asymptotically efficient estimators for self-similar stationary Gaussian noises under high frequency observations. Bernoulli 25 (2019) 1870–1900. [CrossRef] [Google Scholar]
  12. X. Guyon and J. Léon, Convergence en loi des H-variations d’un processus gaussien stationnaire sur R. Ann. Inst. Henri Poincaré - Probab. Statist. B 25 (1989) 265–282. [Google Scholar]
  13. J. Hájek, Local asymptotic minimax and admissibility in estimation, in Proceedings of 6th Berkeley Symposium on Math. Statist. Prob. (1972) 175–194. [Google Scholar]
  14. I. Ibragimov and R. Has’minski, Statistical Estimation: Asymptotic Theory. Springer-Verlag (1981). [CrossRef] [Google Scholar]
  15. J. Istas and G. Lang, Quadratic variations and estimation of the local Hölder index of a Gaussian process. Ann. Instit. Henri Poincaré - Probab. Statist. B 33 (1997) 407–436. [Google Scholar]
  16. R. Kawai, Fisher information for fractional Brownian motion under high-frequency discrete sampling. Commun. Statist. - Theory Methods 42 (2013) 1628–1636. [CrossRef] [Google Scholar]
  17. Y. Kutoyants and A. Motrunich, On multi-step MLE-process for Markov sequences. Metrika 79 (2016) 705–724. [CrossRef] [Google Scholar]
  18. L. Le Cam, Limits of experiments, in Proceedings of the 6th Berkeley Symposium (1972) 245–261. [Google Scholar]
  19. L. Le Cam, On the asymptotic theory of estimation and testing hypothesis, in Proceedings of the 3rd Berkeley Symposium (1956) 355–368. [Google Scholar]
  20. S. Mazur, D. Otryakhin and M. Podolskij, Estimation of the linear fractional stable motion. Bernoulli 26 (2020) 226–252. [CrossRef] [Google Scholar]
  21. R Core Team, R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing Vienna, Austria. Available from: https://www.R-project.org/ (2016). [Google Scholar]
  22. G. Samorodnitsky and M. Taqqu, Stable Non-Gaussian Random Processes. Chapman & Hall (2000). [Google Scholar]
  23. T. Sweeting, Uniform asymptotic normality of the maximum likelihood estimator. Ann. Statist. 8 (1980) 1375–1381. [CrossRef] [Google Scholar]
  24. A. van der Vaart, Asymptotic Statistics. Cambridge University Press (1998). [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.