Exact asymptotic bias for estimators of the Ornstein-Uhlenbeck process

We study the bias and the bias derivative for a family F of asymptotically efficient estimators of the Ornstein-Uhlenbeck process. That family contains the maximum likelihood, the conditional maximum likelihood and the empirical estimators. We show that, if g(θT) is an estimator of g(θ), where θ is the parameter and θT ε F, then, under mild conditions, where cθ is an explicit constant that only depends on the choice of θT. In particular, if θT is one of the three previous estimators, one has. © 2010 Springer Science+Business Media B.V.