SEMINARIO: marted́ 21 febbraio alle ore 11:30 in aula 21 edificio B: "Adaptive estimation for diffusion processes", Prof. Yoichi Nishiyama (The Institute of Statistical Mathematics, Tokyo, Japan)
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.