A consistent approach to least squares estimation of correlation dimension in weak Bernoulli dynamical systems

DOI10.1214/aoap/1177004914zbMath0827.62045OpenAlexW1971512760MaRDI QIDQ1345593

Regis J. Serinko

Publication date: 30 March 1995

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aoap/1177004914

zbMATH Keywords

chaosconsistencydynamical systemsnonlinear dynamicslogistic mapconvergence in measureergodic theoryfractalleast squares procedureU-statisticCantor mapabsolute regularcorrelation dimension estimationGrassberger-Procaccia spatial correlation integralitinerate process

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Fractals (28A80) Ergodic theory (37A99) Limit theorems in probability theory (60F99) Nonparametric inference (62G99)

Related Items (7)

On weighted \(U\)-statistics for stationary processes. ⋮ On the dimension of the boundary of clumps in a multi-type Boolean model ⋮ Limit theorems for U-statistics of Bernoulli data ⋮ A new estimator for information dimension with standard errors and confidence intervals ⋮ Dimension spectra for multbfractal measures with connections to nonparametric density estimation^∗ ⋮ Local correlation dimension of multidimensional stochastic process ⋮ Ergodic theorems arising in correlation dimension estimation.

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