Non parametric bias reduction of diffusion coefficient in integrated diffusion processes

Abstract

In this paper, we propose a non parametric functional estimator for diffusion coefficient in integrated stochastic diffusion process. The asymptotic bias of the kernel type estimator and the new proposed non parametric estimator for diffusion coefficient are developed when the time span is fixed, and we can see that the new non parametric estimator has a smaller asymptotic bias than the kernel estimator. Moreover, the consistency and the asymptotic normality of the new proposed non parametric estimator are explored under some mild conditions.

Keywords:

• Bias reduction
• diffusion coefficient
• kernel type estimator
• non parametric estimator
• integrated process

Acknowledgments

The authors would like to thank the Editor and anonymous referees for their valuable suggestions, which greatly improved our paper.

Additional information

Funding

This research is supported by the NSFC (No. 11461032, No. 11401267), the Program of Qingjiang Excellent Young Talents, Jiangxi University of Science and Technology, and the SF of Jiangxi Provincial Education Department (No. GJJ190461).