Estimation of the Hurst parameter from discrete noisy data

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dc.creatorGloter, Arnaud
dc.creatorHoffmann, Marc
dc.date2007-11-21
dc.date.accessioned2026-07-07T08:49:26Z
dc.date.available2026-07-07T08:49:26Z
dc.descriptionWe estimate the Hurst parameter $H$ of a fractional Brownian motion from discrete noisy data observed along a high frequency sampling scheme. The presence of systematic experimental noise makes recovery of $H$ more difficult since relevant information is mostly contained in the high frequencies of the signal. We quantify the difficulty of the statistical problem in a min-max sense: we prove that the rate $n^{-1/(4H+2)}$ is optimal for estimating $H$ and propose rate optimal estimators based on adaptive estimation of quadratic functionals.
dc.descriptionPublished in at http://dx.doi.org/10.1214/009053607000000316 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0711.3342
dc.identifierhttp://arxiv.org/abs/0711.3342
dc.identifierAnnals of Statistics 2007, Vol. 35, No. 5, 1947-1974
dc.identifierdoi:10.1214/009053607000000316
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144297
dc.subjectStatistics Theory
dc.subject60G18, 62G99, 62F12, 62M09
dc.titleEstimation of the Hurst parameter from discrete noisy data
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