Nonparametric robust function estimation for integrated diffusion processes

This paper considers local M-estimation of the unknown drift and diffusion functions of integrated diffusion processes. We show that under appropriate conditions, the proposed estimators for drift and diffusion functions in the integrated process are consistent, and the conditions that ensure the asymptotic normality of these local M-estimators are also stated. The simulation studies show that the proposed estimators perform better than the kernel estimator in robustness.