Robust estimation via $\gamma$-divergence for diffusion processes

TL;DR

This paper introduces a robust estimation method for diffusion processes affected by outliers in high-frequency data, using $ extgamma$-divergence to improve inference accuracy.

Contribution

It develops a new robust estimator based on $ extgamma$-divergence, analyzing its asymptotic properties and influence functions for diffusion processes.

Findings

The estimator is asymptotically normal.

Influence functions are bounded, indicating robustness.

Method effectively handles outliers in high-frequency data.

Abstract

This paper deals with the problem of outliers in high frequency observation data from diffusion processes. Robust estimation methods are needed because the inclusion of outliers can lead to incorrect statistical inference even in the diffusion process. To construct a robust estimator, we first approximate the transition density of the diffusion process to the Gaussian density by using Kessler's approach and then employ two types of minimum robust divergence estimation methods. In this paper, we provide the asymptotic properties of the robust estimator using $\gamma$-divergence. Furthermore, we derive the conditional influence functions of the estimation using divergences and discuss its boundness.