Estimators of Fractal Dimension: Assessing the Roughness of Time Series and Spatial Data

@article{Gneiting2011EstimatorsOF,
  title={Estimators of Fractal Dimension: Assessing the Roughness of Time Series and Spatial Data},
  author={Tilmann Gneiting and Hana vSevvc'ikov'a and Donald B. Percival},
  journal={Statistical Science},
  year={2011},
  volume={27},
  pages={247-277}
}
The fractal or Hausdorff dimension is a measure of roughness (or smoothness) for time series and spatial data. The graph of a smooth, differentiable surface indexed in $\mathbb{R}^d$ has topological and fractal dimension $d$. If the surface is nondifferentiable and rough, the fractal dimension takes values between the topological dimension, $d$, and $d+1$. We review and assess estimators of fractal dimension by their large sample behavior under infill asymptotics, in extensive finite sample… Expand
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