Estimation of the Hurst parameter from discrete noisy data

• 成果类型: Article
• 署名作者: Gloter, Arnaud; Hoffmann, Marc
• 署名单位: Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053607000000316
• 发表日期: 2007
• 页码: 1947-1974
• 关键词: wavelet coefficients

摘要

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.