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November, 1994 A Consistent Approach to Least Squares Estimation of Correlation Dimension in Weak Bernoulli Dynamical Systems
Regis J. Serinko
Ann. Appl. Probab. 4(4): 1234-1254 (November, 1994). DOI: 10.1214/aoap/1177004914

Abstract

A new approach to the least squares procedure for correlation dimension estimation is suggested. Consistency of the new estimator is established for a class of dynamical systems that includes the Cantor map and the logistic map with parameter value 4. Unlike the proofs of consistency for other estimation procedures, no assumptions are made about the Grassberger-Procaccia spatial correlation integral beyond the existence of the correlation dimension.

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Regis J. Serinko. "A Consistent Approach to Least Squares Estimation of Correlation Dimension in Weak Bernoulli Dynamical Systems." Ann. Appl. Probab. 4 (4) 1234 - 1254, November, 1994. https://doi.org/10.1214/aoap/1177004914

Information

Published: November, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0827.62045
MathSciNet: MR1304784
Digital Object Identifier: 10.1214/aoap/1177004914

Subjects:
Primary: 60F99
Secondary: 28A80 , 53F11 , 62G99

Keywords: $U$-statistic , absolutely regular , chaos , convergence in measure , Fractal , Grassberger-Procaccia spatial correlation integral , itinerate process , nonlinear dynamics

Rights: Copyright © 1994 Institute of Mathematical Statistics

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Vol.4 • No. 4 • November, 1994
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