Computational Aspects Related to Martingale Estimating Functions for a Discretely Observed Diffusion

Martingale estimating functions for a discretely observed diffusion have turned out to provide estimators with nice asymptotic properties. However, their expression usually involves some conditional expectation that has to be evaluated through Monte Carlo simulations giving rise to an approximated estimator. In this work we study, for ergodic models, the asymptotic properties of the approximated estimator and describe the influence of the number of independent simulated trajectories involved in the Monte Carlo method as well as of the approximation scheme used. Our results are of practical relevance to assess the implementation of martingale estimating functions for discretely observed diffusions.