Consistency of the Takens estimator for the correlation dimension

DOI10.1214/aoap/1029962747zbMath0928.62072OpenAlexW2069377542MaRDI QIDQ1305413

Robert M. jun. Burton, Herold G. Dehling, Svetlana Borovkova

Publication date: 11 January 2000

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

Full work available at URL: https://doi.org/10.1214/aoap/1029962747

zbMATH Keywords

U-statisticscorrelation dimensionabsolute regularityergodic sequencesTakens estimator

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Nonparametric estimation (62G05) Central limit and other weak theorems (60F05) Stationary stochastic processes (60G10)

Related Items (13)

On weighted \(U\)-statistics for stationary processes. ⋮ Strong laws for generalized absolute Lorenz curves when data are stationary and ergodic sequences ⋮ Multiscale geometric methods for data sets. I: Multiscale SVD, noise and curvature. ⋮ Some remarks on the ergodic theorem for \(U\)-statistics ⋮ On the variable bandwidth kernel estimation of conditional \(U\)-statistics at optimal rates in sup-norm ⋮ Towards coherent estimation of correlation dimension ⋮ Fractal dimension estimation with persistent homology: a comparative study ⋮ Non-parametric estimation of data dimensionality prior to data compression: the case of the human development index ⋮ Statistical estimation of measure invariants ⋮ Limit theorems for nondegenerate \(U\)-statistics of continuous semimartingales ⋮ Limit theorems for functionals of mixing processes with applications to $U$-statistics and dimension estimation ⋮ A renewal approach to Markovian \(U\)-statistics ⋮ Regeneration-based statistics for Harris recurrent Markov chains

Cites Work

• Measuring the strangeness of strange attractors
• Rigorous statistical procedures for data from dynamical systems
• On U-statistics and v. mise? statistics for weakly dependent processes
• Limiting behavior of U-statistics for stationary, absolutely regular processes
• Strong laws for 𝐿- and 𝑢-statistics
• A Class of Statistics with Asymptotically Normal Distribution
• The Theory of Unbiased Estimation
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