No. 1089

Title:

Semiparametric estimation for ergodic diffusion processes

Author(s):

Nishiyama, Yoichi (The Institute of Statistical Mathematics)

Key words:

Estimating function, nuisance parameter, metric entropy, asymptotic efficiency, ergodic diffusion, discrete observation.

Abstract:

    We consider a semiparametric model for ergodic diffusion process where the drift coefficient contains an unknown finite-dimensional parameter and the diffusion coefficient is an infinite-dimensional nuisance parameter. A uniformly consistent estimator for the diffusion coefficient is given in an explicit way, and by using it we construct an asymptotically normal and efficient estimator for the drift coefficient. This paper implements a general theory established by Nishiyama (2009, to appear in Ann. Statist.).