Key result
Spectral analysis provided the least biased results and lowest variance for estimating the fractal dimension from self-affine signals, whereas correlation and rescaled range analyses yielded seriously biased results.
For estimating fractal dimension from self-affine medical signals, spectral analysis provides the most accurate and least variable results compared to correlation, rescaled range, and relative dispersion methods.
Spectral analysis may warrant preference for fractal dimension estimation in physiological signals; leaves open validation in clinical datasets.
Four methods for estimating the fractal dimension, namely, relative dispersion, correlation, rescaled range, and Fourier (spectral) analysis, are described. Modifications of these methods for use on self-similar or self-affine signals are presented. It is found that correlation analysis and rescaled range analysis yield seriously biased results under many circumstances. Relative dispersion analysis is well suited for long signals. Spectral analysis gives the least biased results, and also has lowest variance in the estimates of the fractal dimension.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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Schepers et al. (1992) studied this question. Methods for estimating fractal dimension (relative dispersion, correlation, rescaled range, Fourier analysis) was evaluated on Bias and variance in estimates of the fractal dimension. Spectral analysis provided the least biased results and lowest variance for estimating the fractal dimension from self-affine signals, whereas correlation and rescaled range analyses yielded seriously biased results.
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