Acta mathematica scientia, Series B >
WAVELET-BASED ESTIMATOR FOR THE HURST PARAMETERS OF FRACTIONAL BROWNIAN SHEET
Received date: 2015-09-22
Revised date: 2016-05-12
Online published: 2017-02-25
Supported by
This work was supported in part by the National Basic Research Program of China (973 Program, 2013CB910200, and 2011CB707802).
It is proposed a class of statistical estimators ?=(?1, …, ?d) 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.
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 . DOI: 10.1016/S0252-9602(16)30126-6
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