Frank M, Keller G, Sporer R (1996)
Publication Type: Journal article, Original article
Publication year: 1996
Book Volume: 6
Pages Range: 5831-5836
We discuss the statistical error in the calculation of the sample correlation integral from a finite sample of points. For this purpose we introduce an estimator of the covariance matrix of these estimators. The application of the method is described and it is shown that only small modifications to a standard Grassberger-Procaccia algorithm are necessary. Testing the method with 100 independent runs of the Hénon system, we show that the errors obtained for the correlation integrals are in good accordance with the sample error. These results are extended to the application to time-continuous systems, in our case the Lorenz system
APA:
Frank, M., Keller, G., & Sporer, R. (1996). Practical implementation of error estimation for the correlation dimension. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 6, 5831-5836. https://dx.doi.org/10.1103/PhysRevE.53.5831
MLA:
Frank, M., Gerhard Keller, and Ralph Sporer. "Practical implementation of error estimation for the correlation dimension." Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 6 (1996): 5831-5836.
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