Estimating functions for noisy observations of ergodic diffusions

Benjamin Favetto (1)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

In this article, general estimating functions for ergodic diffusions sampled at high frequency with noisy observations are presented. The theory is formulated in term of approximate martingale estimating functions based on local means of the observations, and simple conditions are given for rate optimality. The estimation of diffusion parameter is faster that the estimation of drift parameter, and the rate of convergence in the Central Limit Theorem is classical for the drift parameter but not classical for the diffusion parameter. The link with specific minimum contrast estimators is established, as an example.

Mots clés: Estimating functions; Diffusion process; Parametric inference; Discrete time noisy observations; Central limit theorem

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Benjamin Favetto. Estimating functions for noisy observations of ergodic diffusions. 2010. ⟨hal-00531096v2⟩