No. 1093

Title:

Parametric estimation for volatility of ergodic diffusion process with unspecified drift

Author(s):

Nishiyama, Yoichi (The Institute of Statistical Mathematics)

Key words:

Estimating function, asymptotic efficiency, ergodic diffusion, discrete observation.

Abstract:

    We consider a statistical model of one-dimensional ergodic diffusion processes where the diffusion coefficient contains a finite-dimensional parameter of interest and the drift coefficient is not specified. We constract an estimator for the diffusion coefficient not using any information on the drift coefficient, and prove its asymptotic normality. The limit distribution is the same as that of the LAN theory in the case where the drift coefficient is known, and thus our estimator is asymptotically optimal.