Box dimension estimation of multi-dimensional random fields via wavelet shrinkage

Taheriyoun, Ali Reza; Wang, Yazhen

doi:10.4310/sii.2017.v10.n2.a5

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2021

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“…For a stationary Gaussian random field, Wu & Lim (2016) used the decay rate of the spectral density to estimate the fractal dimension. Wang (1997) proposed a wavelet shrinkage estimator for noisy observations of a stochastic process and the extension to N-dimensional random fields was developed by Taheriyoun & Wang (2017). The fractal index has also been estimated as the self-similarity index in a frequency-domain using wavelets for time series data by Ramírez-Cobo et al (2011).…”

Section: Introduction 1general Motivationmentioning

confidence: 99%

The estimation of the fractal dimension of a Gaussian field via Euler characteristic

Taheriyoun

Shafie

2021

Can J Statistics

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Fractal dimension is a useful characteristic for measuring the irregularity of random fields. In this work, we employ the Euler characteristic (EC) of the excursion sets of a field to estimate the fractal dimension of the random field using the roughness of the underlying realization. The EC of a non‐differentiable Gaussian field is either zero or infinity with probability one and hence we employ a weighted smooth version of the field. Under some weak assumptions, the estimator is consistent when the weight function is constant. The results are examined through a simulation study and applied on real data.

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