Recurrence plots (RPs) have proved to be a very versatile tool to analyze temporal dynamics of time series data. However, it has also been conjectured that RPs can be used to model samples of random variables, that is, data that do not contain any temporal dependencies. In the current paper, we show that RPs can indeed be used to mimic nonparametric inferential statistics. Particularly, we use the case of the two-sample Kolmogorov-Smirnov test as a proof-of-concept, showing how such a test can be done based on RPs. Simulations on differences in mean, variance, and shape of two distributions show that the results of the classical two-sample Kolmogorov-Smirnov test and the recurrence-based test for differences in distributions of two independent samples scale well with each other. While the Kolmogorov-Smirnov test seems to be more sensitive in detecting differences in means, the recurrence based test seems to be more sensitive to detect heteroscedasticity and asymmetry. Potential improvements of our approach as well as extensions to tests with individual distributions are discussed.
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Deriving inferential statistics from recurrence plots: A recurrence-based test of differences between sample distributions and its comparison to the two-sample Kolmogorov-Smirnov test
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August 2018
Research Article|
August 28 2018
Deriving inferential statistics from recurrence plots: A recurrence-based test of differences between sample distributions and its comparison to the two-sample Kolmogorov-Smirnov test
Special Collection:
Recurrence Quantification Analysis for Understanding Complex Systems
Sebastian Wallot;
Sebastian Wallot
1
Max Planck Institute for Empirical Aesthetics
, Grüneburgweg 14, 60322 Frankfurt am Main, Germany
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Giuseppe Leonardi
Giuseppe Leonardi
a)
2
Faculty of Psychology, University of Finance and Management
, ul. Pawia 55, 01-030 Warsaw, Poland
a)Author to whom correspondence should be addressed: g.leonardi@vizja.pl, Tel.: +48 22 536-54-11.
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a)Author to whom correspondence should be addressed: g.leonardi@vizja.pl, Tel.: +48 22 536-54-11.
Chaos 28, 085712 (2018)
Article history
Received:
February 05 2018
Accepted:
June 13 2018
Citation
Sebastian Wallot, Giuseppe Leonardi; Deriving inferential statistics from recurrence plots: A recurrence-based test of differences between sample distributions and its comparison to the two-sample Kolmogorov-Smirnov test. Chaos 1 August 2018; 28 (8): 085712. https://doi.org/10.1063/1.5024915
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