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A bootstrap approach to estimating fractal dimensions

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3 Author(s)
T. Mikosch ; Inst. of Stat. & Oper. Res., Victoria Univ., Wellington, New Zealand ; D. Vere-Jones ; Q. Wang

This paper outlines a bootstrap approach to estimating the “correlation dimension” of a fractal measure, from a set of observations on that measure. An important example is estimating the dimension of the attractor of a chaotic system from a set of observations on that system. The method reduces the effects of dependence among the observations, is stable to minor variations in the procedure, and provides a preliminary estimate of the variance of the estimate. Examples from chaotic and stochastic systems show a systematic tendency to underestimate the dimensions from stochastic systems. Extensions to other generalised Renyi dimensions appear to be difficult

Published in:

Acoustics, Speech, and Signal Processing, 1994. ICASSP-94., 1994 IEEE International Conference on  (Volume:vi )

Date of Conference:

19-22 Apr 1994