Statistical error in a chord estimator of correlation dimension: The rule of five''
- Los Alamos National Lab., NM (United States)
- University of Western Ontario, London, ON (Canada). Dept. of Applied Mathematics
The statistical precision of a chord method for estimating dimension from a correlation integral is derived. The optimal chord length is determined, and a comparison is made to other estimators. The simple chord estimator is only 25% less precise than the optimal estimator which uses the full resolution and full range of the correlation integral. The analytic calculations are based on the hypothesis that all pairwise distances between the points in the embedding space are statistically independent. The adequacy of this approximation is assessed numerically, and a surprising result is observed in which dimension estimators can be anomalously precise for sets with reasonably uniform (nonfractal) distributions.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE; DOHHS; USDOE, Washington, DC (United States); Department of Health and Human Services, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 7027608
- Report Number(s):
- LA-UR-92-2972; CONF-9208161-1; ON: DE93000687; CNN: 1-R01-MH47184-01
- Resource Relation:
- Journal Volume: 03; Journal Issue: 03; Conference: 2. bifurcations and chaos workshop on dynamical measures of complexity and chaos, Bryn Mawr, PA (United States), 13-15 Aug 1992
- Country of Publication:
- United States
- Language:
- English
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