Estimating functions for noisy observations of ergodic diffusions

In this article, general estimating functions for ergodic diffusions sam-pled at high frequency with noisy observations are presented. The the-ory is formulated in term of approximate martingale estimating func-tions based on local means of the observations, and simple conditions are given for rate optimality. The estimation of diffusion parameter is faster that the estimation of drift parameter, and the rate of conver-gence in the Central Limit Theorem is classical for the drift parameter but not classical for the diffusion parameter. The link with specific minimum contrast estimators is established, as an example. Key Words: estimating functions, diffusion process, parametric inference, discrete time noisy observations, central limit theore