Shémas de discrétisation anticipatifs et estimation d'une diffusion

Abstract

We propose an estimation method for the drift parameter of an ergodic diffusion observed at constant step δ > 0. Adapting the generalized method of moments (Hansen) to the anticipative and approximate trapezoidal scheme (resp. Simpson's one), we obtain an asymptotically normal and efficient estimator with a bias of order δ 2 (resp. δ 4).