publication . Other literature type . Preprint . Article . 2019

Copula index for detecting dependence and monotonicity between stochastic signals

Kiran Karra; Lamine Mili;
  • Published: 01 Jun 2019
  • Publisher: Elsevier BV
Abstract
This paper introduces a nonparametric copula-based index for detecting the strength and monotonicity structure of linear and nonlinear statistical dependence between pairs of random variables or stochastic signals. Our index, termed Copula Index for Detecting Dependence and Monotonicity (CIM), satisfies several desirable properties of measures of association, including Renyi's properties, the data processing inequality (DPI), and consequently self-equitability. Synthetic data simulations reveal that the statistical power of CIM compares favorably to other state-of-the-art measures of association that are proven to satisfy the DPI. Simulation results with real-wo...
Subjects
free text keywords: Statistics - Machine Learning, Quantitative Biology - Quantitative Methods, Control and Systems Engineering, Theoretical Computer Science, Software, Information Systems and Management, Artificial Intelligence, Computer Science Applications, Mutual information, Random variable, Discrete mathematics, Synthetic data, Estimator, Statistical power, Copula (linguistics), Nonparametric statistics, Mathematics, Markov chain, Algorithm
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Abstract
This paper introduces a nonparametric copula-based index for detecting the strength and monotonicity structure of linear and nonlinear statistical dependence between pairs of random variables or stochastic signals. Our index, termed Copula Index for Detecting Dependence and Monotonicity (CIM), satisfies several desirable properties of measures of association, including Renyi's properties, the data processing inequality (DPI), and consequently self-equitability. Synthetic data simulations reveal that the statistical power of CIM compares favorably to other state-of-the-art measures of association that are proven to satisfy the DPI. Simulation results with real-wo...
Subjects
free text keywords: Statistics - Machine Learning, Quantitative Biology - Quantitative Methods, Control and Systems Engineering, Theoretical Computer Science, Software, Information Systems and Management, Artificial Intelligence, Computer Science Applications, Mutual information, Random variable, Discrete mathematics, Synthetic data, Estimator, Statistical power, Copula (linguistics), Nonparametric statistics, Mathematics, Markov chain, Algorithm
Related Organizations

M. Ahsanullah, V. Nevzorov, and M. Shakil. An Introduction to Order Statistics, volume 3. Atlantis Press, 2013.

T. Bedford and R. Cooke. Vines{a new graphical model for dependent random variables. The Annals of Statistics, 30(4):1031{1068, 08 2002. doi: 10.1214/aos/1031689016.

J. Beirlant, E. Dudewica, L. Gyor , and E. van der Meulen. Nonparametric entropy estimation : An overview. Journal of Statistics, 1997.

P. Bellot, C. Olsen, P. Salembier, A. Oliveras-Verges, and P. Meyer. Netbenchmark: a bioconductor package for reproducible benchmarks of gene regulatory network inference. BMC Bioinformatics, 16(1):312, 2015. doi: 10.1186/s12859-015-0728-4. [OpenAIRE]

D. Lopez-Paz, P. Henning, and B. Scholkopf. The Randomized Dependence Coe cient. In Advances in Neural Information Processing Systems 26. Curran Associates, Inc., 2013.

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F. Vandenhende and P. Lambert. Improved Rank-Based Dependence Measures for Categorical Data. Statistics and Probability Letters, 63(2):157{163, 2003. [OpenAIRE]

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publication . Other literature type . Preprint . Article . 2019

Copula index for detecting dependence and monotonicity between stochastic signals

Kiran Karra; Lamine Mili;