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A new estimator for information dimension with standard errors and confidence intervals

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  • Keller, Gerhard

Abstract

A new least-squares approach to information dimension estimation of the invariant distribution of a dynamical system is suggested. It is computationally similar to the Grassberger-Procaccia algorithm for estimating the correlation dimension over a fixed range of radii. Under mixing assumptions on the observations that are customary for chaotic dynamical systems, the estimator enjoys nearly the same asymptotic normality properties as the Grassberger-Procaccia procedure. Technically, one has to deal with a mixture of U- and L-statistic representations and their modifications for data from deterministic chaotic dynamical systems to estimate smoothly trimmed spatial correlation integrals.

Suggested Citation

  • Keller, Gerhard, 1997. "A new estimator for information dimension with standard errors and confidence intervals," Stochastic Processes and their Applications, Elsevier, vol. 71(2), pages 187-206, November.
    • Handle: RePEc:eee:spapps:v:71:y:1997:i:2:p:187-206
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    Cited by:

    1. Denker, Manfred & Min, Aleksey, 2008. "A central limit theorem for measurements on the logarithmic scale and its application to dimension estimates," Journal of Multivariate Analysis, Elsevier, vol. 99(4), pages 665-683, April.

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