WAVELET-BASED ESTIMATOR FOR THE HURST PARAMETERS OF FRACTIONAL BROWNIAN SHEET

It is proposed a class of statistical estimators H = （H1,… ,Hd） 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 depend...

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Bibliographic Details
Published in:Acta mathematica scientia 2017, Vol.37 (1), p.205-222
Main Author: 吴量 丁义明
Format: Article
Language:English
Subjects:
42C40
60G22
62M40
Brownian
detection of long-range dependence
fractional Brownian sheet
Hurst parameters
Hurst参数
self-similarity
wavelet analysis
分数
多维信号
小波变换
布朗单
模拟数据
统计估计
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Summary:It is proposed a class of statistical estimators H = （H1,… ,Hd） 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 ≥ 1/2, the estimators are accurate, and when Hi 〈 1/2, there are some bias.
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(16)30126-6