DOI: 10.1142/s0218127493000672. STATISTICAL ERROR IN A CHORD ESTIMATOR OF CORRELATION DIMENSION: THE “RULE OF FIVE”

STATISTICAL ERROR IN A CHORD ESTIMATOR OF CORRELATION DIMENSION: THE “RULE OF FIVE”

10.1142/s0218127493000672

Crossref journal-article

World Scientific Pub Co Pte Lt

International Journal of Bifurcation and Chaos (219)

Abstract

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 with 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.

Bibliography

THEILER, J., & LOOKMAN, T. (1993). STATISTICAL ERROR IN A CHORD ESTIMATOR OF CORRELATION DIMENSION: THE âRULE OF FIVE.â International Journal of Bifurcation and Chaos, 03(03), 765â771.

Authors 2

JAMES THEILER (first)
TURAB LOOKMAN (additional)

References 0 Referenced 33

None

Dates

Type	When
Created	20 years, 9 months ago (Nov. 19, 2004, 2:08 a.m.)
Deposited	6 years, 1 month ago (Aug. 6, 2019, 2:22 p.m.)
Indexed	3 months, 1 week ago (May 27, 2025, 1:45 a.m.)
Issued	32 years, 3 months ago (June 1, 1993)
Published	32 years, 3 months ago (June 1, 1993)
Published Online	13 years, 9 months ago (Nov. 20, 2011)
Published Print	32 years, 3 months ago (June 1, 1993)

Funders 0

None

BibTeX

@article{THEILER_1993, title={STATISTICAL ERROR IN A CHORD ESTIMATOR OF CORRELATION DIMENSION: THE “RULE OF FIVE”}, volume={03}, ISSN={1793-6551}, url={http://dx.doi.org/10.1142/s0218127493000672}, DOI={10.1142/s0218127493000672}, number={03}, journal={International Journal of Bifurcation and Chaos}, publisher={World Scientific Pub Co Pte Lt}, author={THEILER, JAMES and LOOKMAN, TURAB}, year={1993}, month=jun, pages={765–771} }

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