Title: Non-adaptive estimation for a degenerate diffusion process
Authors: Arnaud Gloter - Universite d Evry Val d Essonne (France)
Nakahiro Yoshida - University of Tokyo (Japan) [presenting]
Abstract: A multi-dimensional ergodic diffusion process specified by a system of stochastic differential equations is considered. The first component has a non-degenerate diffusion coefficient, and the second component has no diffusion coefficient. Each coefficient has an unknown vector parameter, and we estimate these parameters based on long-term high-frequency observations. While we focused on the adaptive method last year, here we discuss a non-adaptive method. The convergence rates of the diffusion parameter and the drift parameter in the non-degenerate component are the same as the usual ones, but the asymptotic variance is improved. The convergence of the estimator for the parameter in the degenerate component is much faster than the others. The non-adaptive method does not require any initial estimators and achieves the same asymptotic normality as the adaptive method.