Estimation for Discretely Observed Small Diffusions Based on Approximate Martingale Estimating Functions

We consider an asymptotically efficient estimator of the drift parameter for a multi-dimensional diffusion process with small dispersion parameter "ϵ". In the situation where the sample path is observed at equidistant times "k"/"n", "k" = 0, 1, …, "n", we study asymptotic properties of an "M"-estimator derived from an approximate martingale estimating function as "ϵ" tends to 0 and "n" tends to ∞ simultaneously. Copyright 2004 Board of the Foundation of the Scandinavian Journal of Statistics..