The LE-statistic — Paper Nexus

Summary

A quantity called LE-statistic is introduced that is an easily computable functional of ordinal data with versatile applications and usefulness as a statistic in a nonparametric independence test of paired samples, and as a complexity measure of a scalar time series.

Keywords

Lyapunov exponent, Statistic, Nonparametric statistics, Mathematics, Chaotic

References

A symbolic test for testing independence between time seriesMariano Matilla‐García, José Miguel Rodríguez, Manuel Ruiz Marín — 2010
A standardized approach to the Kolmogorov–Sinai entropyKarsten Keller, Mathieu Sinn — 2009
A NEW MEASURE OF RANK CORRELATIONM. G. Kendall — 1938
Ergodic theory of chaos and strange attractorsJean‐Pierre Eckmann, David Ruelle — 1985
CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORYYa. B. Pesin — 1977
The permutation entropy rate equals the metric entropy rate for ergodic information sources and ergodic dynamical systemsJosé M. Amigó, Matthew B. Kennel, Ljupčo Kocarev — 2005
Permutation entropy: a natural complexity measure for time series.Christoph Bandt, Bernd Pompe — 2002
Generating partitions for the dissipative Hénon mapPeter Grassberger, Hölger Kantz — 1985
Entropy of interval maps via permutationsChristoph Bandt, Gerhard Keller, Bernd Pompe — 2002
Permutation entropy: One concept, two approachesJosé M. Amigó, Karsten Keller — 2013
An inequality for the entropy of differentiable mapsDavid Ruelle — 1978
General intelligence Objectively Determined and MeasuredC. Spearman — 1904
The metric entropy of diffeomorphisms Part I: Characterization of measures satisfying Pesin's entropy formulaF. Ledrappier, Lai-Sang Young — 1985
Permutation Complexity in Dynamical SystemsJosé M. Amigó — 2010
Nonlinear Time Series AnalysisH. Kantz, T. Schreiber — 2005
Copula Theory: An IntroductionF. Durante, C. Sempi — 2010
Copula-Based Measures of Multivariate AssociationF. Schmid, R. Schmidt, Thomas Blumentritt — 2010

Cited by

Change-Point Detection Using the Conditional Entropy of Ordinal Patternsعلی حندقیان, علی لطفعلیان, آیدا آرای — 2015
Change-Point Detection using the Conditional Entropy of Ordinal PatternsKarsten Keller, Anton M. Unakafov — 2018

Related papers

Approximating Lyapunov Exponents of Discrete Dynamical SystemsWadia Faid Hassan Al-shameri — 2019
A General Approach to Hypothesis Testing for Nonparametric TestsMichael R. Harwell — 1990
On unbiasedness and biasedness of the Wilcoxon and some nonparametric testsHidetoshi Murakami, Seong‐Keon Lee — 2022
Differentially Private Nonparametric Hypothesis TestingSimon Couch, Zeki Kazan, Kaiyan Shi — 2019
Nonparametric statistical testing of EEG- and MEG-data.Eric Maris, Robert Oostenveld — 2007
A nonparametric test for slowly-varying nonstationaritiesDouglas Baptista de Souza, Jocelyn Chanussot, Anne‐Catherine Favre — 2018
Possibility Measure of Accepting Statistical HypothesisJung-Lin Hung, Cheng‐Che Chen, Chun-Mei Lai — 2020