JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Minimum Density Power Divergence Estimator for Diffusion Parameter in Discretely Observed Diffusion Processes
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Minimum Density Power Divergence Estimator for Diffusion Parameter in Discretely Observed Diffusion Processes
Song, Jun-Mo; Lee, Sang-Yeol; Na, Ok-Young; Kim, Hyo-Jung;
  PDF(new window)
 Abstract
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.
 Keywords
ergodic diffusion processes;Brownian motion;minimum density power divergence estimator;robustness;
 Language
English
 Cited by
 References
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 crossref(new window)

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 crossref(new window)

3.
Beran, R. (1977). Minimum Hellinger distance estimates for parametric models. The Annals of Statistics, 5, 445-463 crossref(new window)

4.
Cao, R., Cuevas, A. and Fraiman, R. (1995). Minimum distance density-based estimation. Computational Statistics & Data Analysis, 20, 611-631 crossref(new window)

5.
Dacunha-Castelle, D. and Florens-Zmirou, D. (1986). Estimation of the coefficients of a diffusion from discrete observations. Stochastics, 19, 263-284 crossref(new window)

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 crossref(new window)

12.
Kessler, M. (2000). Simple and explicit estimating functions for a discretely observed diffusion process. Scandinavian Journal of Statistics, 27, 65-82 crossref(new window)

13.
Kessler, M. and Serensen, M. (1999). Estimating equations based on eigenfunctions for a discretely observed diffusion process. Bernoulli, 5, 299-314 crossref(new window)

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 crossref(new window)

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 crossref(new window)

19.
Simpson, D. G. (1987). Minimum Hellinger distance estimation for the analysis of count data. Journal of the American Statistical Association, 82, 802-807 crossref(new window)

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 crossref(new window)

22.
Warwick, J. and Jones, M. C. (2005). Choosing a robustness tuning parameter. Journal of Statistical Computation and Simulation, 75, 581-588 crossref(new window)

23.
Yoshida, N. (1992). Estimation for diffusion processes from discrete observation. Journal of Multivariate Analysis, 41, 220-242 crossref(new window)