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

作     者：吴量 丁义明 

作者机构：Wuhan Institute of Physics and MathematicsChinese Academy of SciencesWuhan 430071China University of Chinese Academy of SciencesBeijing 100049China Department of MathematicsWuhan Institute of TechnologyWuhan 430070China Key Laboratory of Magnetic Resonance in Biological SystemsWuhan Institute of Physics and MathematicsChinese Academy of SciencesWuhan 430071China 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2017年第37卷第1期

页      面：205-222页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported in part by the National Basic Research Program of China(973 Program 2013CB910200 and 2011CB707802) 

主　　题：detection of long-range dependence self-similarity Hurst parameters waveletanalysis fractional Brownian sheet 

摘      要：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.