Moment estimation for ergodic diffusion processes

TL;DR

This paper develops efficient methods for estimating moments of ergodic diffusion processes, providing lower bounds, constructing estimators, and analyzing their higher order properties through Edgeworth expansions.

Contribution

It introduces new asymptotically efficient estimators for moments and parameters in ergodic diffusion processes, with both nonparametric and parametric approaches.

Findings

Derived lower bounds for estimation risk

Constructed asymptotically efficient estimators

Analyzed higher order properties via Edgeworth expansion

Abstract

We investigate the moment estimation for an ergodic diffusion process with unknown trend coefficient. We consider nonparametric and parametric estimation. In each case, we present a lower bound for the risk and then construct an asymptotically efficient estimator of the moment type functional or of a parameter which has a one-to-one correspondence to such a functional. Next, we clarify a higher order property of the moment type estimator by the Edgeworth expansion of the distribution function.