Wavelet-based estimator for the hurst parameters of fractional brownian sheet

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• 作者：Liang WU^a ; ^b ; ^{wuliangshine@gmail.com} ; Yiming DING^c ; ^d ; ^{ding@wipm.ac.cn}
• 关键词：detection of long-range dependence ; self-similarity ; Hurst parameters ; wavelet analysis ; fractional Brownian sheet
• 刊名：Acta Mathematica Scientia
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：37
• 期：1
• 页码：205-222
• 全文大小：253 K
• 卷排序：37

文摘

It is proposed a class of statistical estimators Ĥ = (Ĥ1, … Ĥ) for the Hurst parameters H =(H1, …, Hd) of fractional Brownian field via multi-dimensional wavelet analysis and least squares, which are asymptotically normal. These estimators can be used to detect self-similarity and long-range dependence in multi-dimensional signals, which is important in texture classification and improvement of diffusion tensor imaging (DTI) of nuclear magnetic resonance (NMR). Some fractional Brownian sheets will be simulated and the simulated data are used to validate these estimators. We find that when Hi ≥ ½, the estimators are accurate, and when Hi < ½, there are some bias.