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

doi:10.1016/S0252-9602(16)30126-6

Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (1): 205-222.doi: 10.1016/S0252-9602(16)30126-6

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

Liang WU^1,2, Yiming DING^3,4

1. Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China;
2. University of Chinese Academy of Sciences, Beijing 100049, China;
3. Department of Mathematics, Wuhan Institute of Technology, Wuhan 430070, China;
4. Key Laboratory of Magnetic Resonance in Biological Systems, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China

Received:2015-09-22 Revised:2016-05-12 Online:2017-02-25 Published:2017-02-25
Contact: Yiming DING,E-mail:ding@wipm.ac.cn E-mail:ding@wipm.ac.cn
About author:Liang WU,E-mail:wuliangshine@gmail.com
Supported by:
This work was supported in part by the National Basic Research Program of China (973 Program, 2013CB910200, and 2011CB707802).

Abstract

Abstract:

It is proposed a class of statistical estimators ?=(?₁, …, ?_d) for the Hurst parameters H=(H₁,…,H_d) 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 H_i≥1/2, the estimators are accurate, and when H_i<1/2, there are some bias.

Key words: detection of long-range dependence, self-similarity, Hurst parameters, wavelet analysis, fractional Brownian sheet

Liang WU, Yiming DING. WAVELET-BASED ESTIMATOR FOR THE HURST PARAMETERS OF FRACTIONAL BROWNIAN SHEET[J].Acta mathematica scientia,Series B, 2017, 37(1): 205-222.

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

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