Open Access
April 2020 Hurst function estimation
Jinqi Shen, Tailen Hsing
Ann. Statist. 48(2): 838-862 (April 2020). DOI: 10.1214/19-AOS1825


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.


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Jinqi Shen. Tailen Hsing. "Hurst function estimation." Ann. Statist. 48 (2) 838 - 862, April 2020.


Received: 1 June 2018; Revised: 1 January 2019; Published: April 2020
First available in Project Euclid: 26 May 2020

zbMATH: 07241571
MathSciNet: MR4102678
Digital Object Identifier: 10.1214/19-AOS1825

Primary: 62G05 , 62G20
Secondary: 62M30

Keywords: infill asymptotics , Minimax rate , Multifractional Brownian motion , nonparametric estimation

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.48 • No. 2 • April 2020
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