INCREMENT-BASED ESTIMATORS OF FRACTAL DIMENSION FOR TWO-DIMENSIONAL SURFACE DATA

In a recent paper, Kent and Wood (1997) investigated some new increment- based estimators of the fractal dimension of a stationary Gaussian process. In the present paper, we extend this work by constructing increment-based estimators based on two-dimensional sampling of surface data (as opposed to the one dimen- sional, or line transect, sampling previously considered). Much of our attention is focussed on two new estimators based on the "square increment". The practical performance of these estimators is examined in the study of several real datasets and via simulation. We also provide a detailed theoretical study of their properties in both Gaussian and non-Gaussian settings. Perhaps surprisingly, it turns out that there are differences in the limit theory in the Gaussian and non-Gaussian cases.

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