Bias-correction of the maximum likelihood estimator for the   $\alpha$-Brownian bridge
  The $\alpha$-Brownian bridge, or scaled Brownian bridge, is a generalization of the Brownian bridge with a scaling parameter that determines how strong the force that pulls the process back to 0 is. The bias of the maximum likelihood estimator of the parameter $\alpha$ is derived and a bias-correction that improves the estimator substantially is proposed. The properties of the bias-corrected estimator and four Bayesian estimators based on non-informative priors are evaluated in a simulation study. 
Maik G\"orgens and M{\aa}ns Thulin
math.ST stat.ME stat.TH