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Abstract and Applied Analysis
Volume 2014, Article ID 635917, 14 pages
http://dx.doi.org/10.1155/2014/635917
Research Article

Nonparametric Regression with Subfractional Brownian Motion via Malliavin Calculus

School of Mathematics and Statistics, Nanjing Audit University, 86 West Yushan Road, Pukou, Nanjing 211815, China

Received 27 November 2013; Accepted 13 December 2013; Published 6 February 2014

Academic Editor: Litan Yan

Copyright © 2014 Yuquan Cang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. P. Hansen, “Large sample properties of generalized method of moments estimators,” Econometrica, vol. 50, pp. 1029–1054, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. D. W. K. Andrewa and C. J. McDermott, “Nonlinear econometric models with deterministically trending variables,” Reiew of Economic Studies, vol. 62, pp. 343–360, 1995. View at Google Scholar
  3. J. M. Wooldridge, “Chapter 45 Estimation and inference for dependent processes,” Handbook of Econometrics, vol. 4, pp. 2639–2738, 1994. View at Publisher · View at Google Scholar · View at Scopus
  4. C. W. J. Granger, “Nonlinear relationships between extended-memory variables,” Econometrica, vol. 63, no. 2, pp. 265–280, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. H. A. Karlsen, T. Myklebust, and D. Tjøstheim, “Nonparametric estimation in a nonlinear cointegration type model,” Annals of Statistics, vol. 35, no. 1, pp. 252–299, 2007. View at Publisher · View at Google Scholar · View at Scopus
  6. Q. Wang and P. C. B. Phillips, “Asymptotic theory for local time density estimation and nonparametric cointegrating regression,” Econometric Theory, vol. 25, no. 3, pp. 710–738, 2009. View at Publisher · View at Google Scholar · View at Scopus
  7. S. Bourguin and C. A. Tudor, “Asymptotic theory for fractional regression models via malliavin calculus,” Journal of Theoretical Probability, vol. 25, no. 2, pp. 536–564, 2012. View at Publisher · View at Google Scholar · View at Scopus
  8. L. Yan and G. Shen, “On the collision local time of sub-fractional Brownian motions,” Statistics and Probability Letters, vol. 80, no. 5-6, pp. 296–308, 2010. View at Publisher · View at Google Scholar · View at Scopus
  9. L. Yan, G. Shen, and K. He, “Itô's formula for a sub-fractional Brownian motion,” Communications on Stochastic Analysis, vol. 5, no. 1, pp. 135–159, 2011. View at Google Scholar
  10. T. Bojdecki, L. G. Gorostiza, and A. Talarczyk, “Fractional Brownian density process and its self-intersection local time of order k,” Journal of Theoretical Probability, vol. 17, no. 3, pp. 717–739, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. T. Bojdecki, L. G. Gorostiza, and A. Talarczyk, “Limit theorems for occupation time fluctuations of branching systems I: long-range dependence,” Stochastic Processes and their Applications, vol. 116, no. 1, pp. 1–18, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  12. T. Bojdecki, L. G. Gorostiza, and A. Talarczyk, “Some extensions of fractional brownian motion and sub-fractional browian motion related to particle systems,” Electronic Communications in Probability, vol. 12, pp. 161–172, 2007. View at Google Scholar · View at Scopus
  13. J. Liu and L. Yan, “Remarks on asymptotic behavior of weighted quadratic variation of subfractional Brownian motion,” Journal of the Korean Statistical Society, vol. 41, no. 2, pp. 177–187, 2012. View at Publisher · View at Google Scholar · View at Scopus
  14. J. Liu, L. Yan, Z. Peng, and D. Wang, “Remarks on confidence intervals for self-similarity parameter of a subfractional brownian motion,” Abstract and Applied Analysis, vol. 2012, Article ID 804942, 14 pages, 2012. View at Publisher · View at Google Scholar · View at Scopus
  15. C. Tudor, “Inner product spaces of integrands associated to subfractional Brownian motion,” Statistics and Probability Letters, vol. 78, no. 14, pp. 2201–2209, 2008. View at Publisher · View at Google Scholar · View at Scopus
  16. D. Nualart, Malliavin Calculus and Related Topics, Springer, New York, NY, USA, 2nd edition, 2006.
  17. C. Tudor, “Some properties of the sub-fractional Brownian motion,” Stochastics, vol. 79, no. 5, pp. 431–448, 2007. View at Publisher · View at Google Scholar · View at Scopus
  18. M. Eddahbi, R. Lacayo, J. L. Solé, J. Vives, and C. A. Tudor, “Regularity of the local time for the d fractional Brownian motion with N,” Stochastic Analysis and Applications, vol. 23, no. 2, pp. 383–400, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus