Approximate martingale estimating functions for stochastic differential equations with small noises

An approximate martingale estimating function with an eigenfunction is proposed for an estimation problem about an unknown drift parameter for a one-dimensional diffusion process with small perturbed parameter εε from discrete time observations at nn regularly spaced time points k/nk/n, k=0,1,…,nk=0,1,…,n. We show asymptotic efficiency of an MM-estimator derived from the approximate martingale estimating function as ε→0ε→0 and n→∞n→∞ simultaneously.