Abstract: In this paper, we consider robust estimation of the dispersion parameter in discretely observed diffusion processes. To construct a robust estimator, we first approximate the transition density of the diffusion process to the Gaussian density by using Kessler (1997) approach and then employ Basu et al. (1998) minimum density power divergence (MDPD) estimation method. It is shown that, under regularity conditions, the MDPD estimator is strongly consistent and asymptotically normal. Through a simulation study, we compared the performances of the MDPD estimator and the quasi-maximum likelihood (QML) estimator based on the approximated transition density. Numerical results demonstrate that the proposed estimator has strong robust properties with little loss in asymptotic efficiency relative to the QML estimator.

Key words and phrases: Diffusion processes, dispersion parameter, minimum density power divergence estimator, robust estimation.