Statistical moments of Gaussian kernel correlation sum and weighted least square estimator of correlation dimension and noise level

DOI10.1016/j.jspi.2017.08.001zbMath1377.62178OpenAlexW2747173403MaRDI QIDQ1681049

Zouhaier Dhifaoui

Publication date: 17 November 2017

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jspi.2017.08.001

zbMATH Keywords

time seriesconfidence intervalU-statisticscorrelation dimensionsignal to noise ratio (SNR)noise levelGaussian kernel correlation integralGaussian kernel correlation sumnon-central chi squared random variablepolynomials chaos decomposition

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Parametric tolerance and confidence regions (62F25) Asymptotic distribution theory in statistics (62E20) Non-Markovian processes: estimation (62M09)

Related Items

Recognition of the scale-free interval for calculating the correlation dimension using machine learning from chaotic time series

Uses Software

• KELLEY

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Is correlation dimension a reliable proxy for the number of dominant influencing variables for modeling risk of arsenic contamination in groundwater?
• Measuring the strangeness of strange attractors
• State space reconstruction in the presence of noise
• Time series: theory and methods.
• The delay vector variance method for detecting determinism and nonlinearity in time series
• Dynamical integral transform on fractal sets and the computation of entropy
• Distinguishing random and deterministic systems: Abridged version
• The Lorenz equations: bifurcations, chaos, and strange attractors
• Effective scaling regime for computing the correlation dimension from chaotic time series
• Improvement of \(K_ 2\)-entropy calculations by means of dimension scaled distances
• An equation for continuous chaos
• Robust to noise and outliers estimator of correlation dimension
• Deterministic nonlinearity in ventricular fibrillation
• Determinism in Financial Time Series
• A NEW IRREGULARITY CRITERION FOR DISCRIMINATION OF STOCHASTIC AND DETERMINISTIC TIME SERIES
• Integrated wavelets on fractal sets. I. The correlation dimension
• The noncentral chi-squared distribution with zero degrees of freedom and testing for uniformity
• A new criterion to distinguish stochastic and deterministic time series with the Poincaré section and fractal dimension
• Resolving statistical uncertainty in correlation dimension estimation
• Univariate Discrete Distributions
• TIME SERIES ANALYSIS OF ECG: A POSSIBILITY OF THE INITIAL DIAGNOSTICS