Annals of Statistics

Hurst function estimation

Jinqi Shen and Tailen Hsing

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Abstract

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.

Article information

Source
Ann. Statist., Volume 48, Number 2 (2020), 838-862.

Dates
Received: June 2018
Revised: January 2019
First available in Project Euclid: 26 May 2020

Permanent link to this document
https://projecteuclid.org/euclid.aos/1590480036

Digital Object Identifier
doi:10.1214/19-AOS1825

Mathematical Reviews number (MathSciNet)
MR4102678

Subjects
Primary: 62G05: Estimation 62G20: Asymptotic properties
Secondary: 62M30: Spatial processes

Keywords
Infill asymptotics minimax rate multifractional Brownian motion nonparametric estimation

Citation

Shen, Jinqi; Hsing, Tailen. Hurst function estimation. Ann. Statist. 48 (2020), no. 2, 838--862. doi:10.1214/19-AOS1825. https://projecteuclid.org/euclid.aos/1590480036


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References

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Supplemental materials

  • Supplement to “Hurst function estimation”. This supplemental material includes all the proofs not included in the paper.