HURST FUNCTION ESTIMATION

• 成果类型: Article
• 署名作者: Shen, Jinqi; Hsing, Tailen
• 署名单位: University of Michigan System; University of Michigan
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1825
• 发表日期: 2020
• 页码: 838-862
• 关键词: fractional brownian motions

摘要

This paper considers a wide range of issues concerning the estimation of the Hurst function of a multifractional Brownian motion when the process is observed on a regular grid. A theoretical lower bound for the minimax risk of this inference problem is established for a wide class of smooth Hurst functions. We also propose a new nonparametric estimator and show that it is rate optimal. Implementation issues of the estimator including how to overcome the presence of a nuisance parameter and choose the tuning parameter from data will be considered. An extensive numerical study is conducted to compare our approach with other approaches.