No. 1098

Title:

Estimation for the invariant density of an ergodic diffusion process based on high frequency data

Author(s):

Nishiyama, Yoichi (The Institute of Statistical Mathematics)

Key words:

Kernel density estimator, weak convergence, asymptotic efficiency.

Abstract:

    Let a one-dimensional ergodic diffusion process $ X $ be observed at time points $ 0=t_0^n < t_1^n < \cdots < t_n^n $ such that $ t_n^n \to \infty $ and $ n \Delta_n^{1+p}\to 0 $, where $ \Delta_n=\max_{1 \leq i \leq n}|t_i^n-t_{i-1}^n| $ and $ p \in (0,1) $ is a constant depending also on the smoothness of the invariant density. We propose a kernel-type estimator for the invariant density based on this data, and prove that it is asymptotically normal and asymptotically efficient in a functional sense.