Communications for Statistical Applications and Methods

  • 제14권2호
  • /
  • Pages.267-280
  • /
  • 2007
  • /
  • 2287-7843(pISSN)
  • /
  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지
DOI QR코드

DOI QR Code

Minimum Density Power Divergence Estimator for Diffusion Parameter in Discretely Observed Diffusion Processes

  • Song, Jun-Mo (Department of Statistics, Seoul National University) ;
  • Lee, Sang-Yeol (Department of Statistics, Seoul National University) ;
  • Na, Ok-Young (Department of Statistics, Seoul National University) ;
  • Kim, Hyo-Jung (Department of Statistics, Seoul National University)
  • 발행 : 2007.08.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we consider the robust estimation for diffusion processes when the sample is observed discretely. As a robust estimator, we consider the minimizing density power divergence estimator (MDPDE) proposed by Basu et al. (1998). It is shown that the MDPDE for diffusion process is weakly consistent. A simulation study demonstrates the robustness of the MDPDE.

키워드

참고문헌

  1. Basu, S. and Lindsay, B. G. (1994). Minimum disparity estimation for continuous models: efficiency, distributions and robustness. Annals of the Institute of Statistical Mathematics, 46, 683-705 https://doi.org/10.1007/BF00773476
  2. Basu, A., Harris, I. R., Hjort, N. L. and Jones, M. C. (1998). Robust and efficient estimation by minimizing a density power divergence. Biometrika, 85, 549-559 https://doi.org/10.1093/biomet/85.3.549
  3. Beran, R. (1977). Minimum Hellinger distance estimates for parametric models. The Annals of Statistics, 5, 445-463 https://doi.org/10.1214/aos/1176343842
  4. Cao, R., Cuevas, A. and Fraiman, R. (1995). Minimum distance density-based estimation. Computational Statistics & Data Analysis, 20, 611-631 https://doi.org/10.1016/0167-9473(94)00065-4
  5. Dacunha-Castelle, D. and Florens-Zmirou, D. (1986). Estimation of the coefficients of a diffusion from discrete observations. Stochastics, 19, 263-284 https://doi.org/10.1080/17442508608833428
  6. Florens-Zmirou, D. (1989). Approximate discrete-time schemes for statistics of diffusion processes. Statistics, 20, 547-557
  7. Friedman, A. (1975). Stochastic Differential Equations and Applications. Academic Press, INC
  8. Genon-Catalot, V. and Jacod, J. (1993). On the estimation of the diffusion coefficient for multidimensional diffusion processes. Annales Institut Henri Poincare Probabilites et Statistiques, 29, 119-151
  9. Hong, C. and Kim, Y. (2001). Automatic selection of the tuning parameter in the minimum density power divergence estimation. Journal of the Korean Statistical Society, 30, 453-465
  10. Ibragimov, I. A. and Has'minskii, R. Z. (1981). Statistical Estimation Asymptotic Theory. Springer-Verlag, New York
  11. Kessler, M. (1997). Estimation of an ergodic diffusion from discrete observations. Scandinavian Journal of Statistics, 24, 211-229 https://doi.org/10.1111/1467-9469.00059
  12. Kessler, M. (2000). Simple and explicit estimating functions for a discretely observed diffusion process. Scandinavian Journal of Statistics, 27, 65-82 https://doi.org/10.1111/1467-9469.00179
  13. Kessler, M. and Serensen, M. (1999). Estimating equations based on eigenfunctions for a discretely observed diffusion process. Bernoulli, 5, 299-314 https://doi.org/10.2307/3318437
  14. Kutoyants, Y. (2004). Statistical Inference for Ergodic Diffusion Processes. Springer-Verlag, New York
  15. Lee, S. and Na, O. (2005). Test for parameter change based on the estimator minimizing density-based divergence measures. Annals of the Institute of Statistical Mathematics, 57, 553-573 https://doi.org/10.1007/BF02509239
  16. Lee, S. and Song, J. (2006). Minimum density power divergence estimator for diffusion processes. submitted for publication
  17. Prakasa Rao, B. L. S. (1999). Statistical Inference for Diffusion Type Processes. Arnold, London
  18. Masuda, H. (2005). Simple estimators for parametric Markovian trend of ergodic processes based on sampled data. Journal of The Japan Statistical Society, 35, 147-170 https://doi.org/10.14490/jjss.35.147
  19. Simpson, D. G. (1987). Minimum Hellinger distance estimation for the analysis of count data. Journal of the American Statistical Association, 82, 802-807 https://doi.org/10.2307/2288789
  20. Song, J. and Lee, S. (2006). Test for parameter change in discretely observed diffusion processes. submitted for publication
  21. Tamura, R. N. and Boos, D. D. (1986). Minimum Hellinger distance estimation for multivariate location and covariance. Journal of the American Statistical Association, 81, 223-239 https://doi.org/10.2307/2287994
  22. Warwick, J. and Jones, M. C. (2005). Choosing a robustness tuning parameter. Journal of Statistical Computation and Simulation, 75, 581-588 https://doi.org/10.1080/00949650412331299120
  23. Yoshida, N. (1992). Estimation for diffusion processes from discrete observation. Journal of Multivariate Analysis, 41, 220-242 https://doi.org/10.1016/0047-259X(92)90068-Q