J. Japan Statist. Soc., Vol. 33 (No. 2), pp. 157-167, 2003
Abstract. We consider an efficient estimation of an unknown parameter appearing in both the drift and the diffusion coefficient for a d-dimensional dynamical system with small noise. Asymptotic properties of an M-estimator obtained from an approximate quadratic martingale estimating function are stated. The sample path is observed at equidistant times k/n, k=0,1, …,n. The type of asymptotics considered is when a small dispersion parameter e goes to 0 and n goes to ∞ simultaneously.
Key words and phrases: Discrete time observation, dynamical systems with small noise, M-estimator, parametric inference, quadratic martingale estimating function