## Annals of Statistics

### Hurst function estimation

#### 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
Revised: January 2019
First available in Project Euclid: 26 May 2020

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

#### 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

#### References

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#### Supplemental materials

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