Estimation of the Hurst parameter from discrete noisy data

Details Estimation of the Hurst parameter from discrete noisy data Estimation of the Hurst parameter from discrete noisy data

2007-11-21

arxiv.org/abs/0711.3342v1

Annals of Statistics 2007, Vol. 35, No. 5, 1947-1974

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/009053607000000316 the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053607000000316

We 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.

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