Hurst function estimation. (English) Zbl 1453.62433

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.


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
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