J. Japan Statist. Soc., Vol. 33 (No. 2), pp. 157-167, 2003

Estimation for dynamical systems with small noise from discrete observations

Masayuki Uchida

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

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