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Shen, Jinqi; Hsing, Tailen

Hurst function estimation. (English) Zbl 1453.62433

Ann. Stat. 48, No. 2, 838-862 (2020).
The authors consider the problem to estimate the Hurst function of a multifractional Brownian motion which is observed on a regular grid. The results include a lower bound on the estimation rate and the construction of a rate optimal nonparametric estimator. The variance multiplier \(\sigma^2\) is either assumed to be known or estimated as well. The authors discuss the implementation of the estimator in details and study its performance in extensive numerical simulations.
Reviewer: Frank Werner (Würzburg)

MSC:

62G05 Nonparametric estimation
62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
62M30 Inference from spatial processes
60G22 Fractional processes, including fractional Brownian motion
62-08 Computational methods for problems pertaining to statistics

Keywords:

infill asymptotics; minimax rate; multifractional Brownian motion; nonparametric estimation
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Full Text: DOI Euclid

References:

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