Abstract
We consider a semiparametric estimation problem in an ergodic diffusion process model, where the drift coefficient contains an unknown finite-dimensional parameter of interest and the diffusion coefficient does a nuisance parameter with infinite-dimension.
We propose two kinds of approaches, namely, semiparametric Z- and Bayes estimations. Both approaches bring us some adaptive estimators, in the sense that their asymptotic distributions of the estimators for the drift coefficient coincide with the optimal one in the Hajek-Le Cam theory when the diffusion coefficient is known.