 A new estimator for information dimension with standard errors and confidence intervalsGerhard Keller Stochastic Processes and their Applications, 1997, vol. 71, issue 2, 187-206 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. Keywords: Information; dimension; Local; dimension; Smoothly; trimmed; spatial; correlation; integral; U-statistic; L-statistic; Asymptotic; normality; Chaotic; dynamical; system; Absolute; regularity; Henon-system (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:71:y:1997:i:2:p:187-206 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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