A Connection between Correlation and Contingency

Hirschfeld, H. O.

doi:10.1017/s0305004100013517

Cited by 460 publications

(231 citation statements)

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“…It was first introduced by Hirschfeld (1935) and Gebelein (1941), and then studied by Rényi (1959). Recently it has become increasingly popular, see Papadatos and Xifara (2013), Papadatos (2014), López Blázquez and Salamanca Miño (2014), Huang and Zhu (2016).…”

Section: Important Dependence Measuresmentioning

confidence: 99%

Four simple axioms of dependence measures

Móri

Székely

2018

Metrika

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Recently new methods for measuring and testing dependence have appeared in the literature. One way to evaluate and compare these measures with each other and with classical ones is to consider what are reasonable and natural axioms that should hold for any measure of dependence. We propose four natural axioms for dependence measures and establish which axioms hold or fail to hold for several widely applied methods. All of the proposed axioms are satisfied by distance correlation. We prove that if a dependence measure is defined for all bounded nonconstant real valued random variables and is invariant with respect to all one-to-one measurable transformations of the real line, then the dependence measure cannot be weakly continuous. This implies that the classical maximal correlation cannot be continuous and thus its application is problematic. The recently introduced maximal information coefficient has the same disadvantage. The lack of weak continuity means that as the sample size increases the empirical values of a dependence measure do not necessarily converge to the population value.

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Section: Important Dependence Measuresmentioning

confidence: 99%

Four simple axioms of dependence measures

Móri

Székely

2018

Metrika

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“…orange sample). For a more comprehensive overview of their power, pros and cons, the contingency tables made up by the total number per class of True Positives, True Negatives (TN, the number of pixels correctly identified as not belonging to the z-th category), False Positives and False Negatives, resulting from the distinct methodologies, were investigated by means of Correspondence Analysis (CA) [53], which is conceptually similar to PCA, but was proposed for categorical rather than continuous data processing. Figures 5.3a, 5.3b and 5.3c vi .…”

Section: Comparative Studymentioning

confidence: 99%

Two-stage least squares and indirect least squares algorithms for simultaneous equations models

López-Espín

Vidal

Giménez

2012

Journal of Computational and Applied Mathematics

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“…The basic idea of this approach is to find such transformations θ(Y ) and φ(X) that the absolute value of the correlation coefficient between the transformed variables is maximized. This leads to the maximal correlation [Hirschfeld, 1935;Gebelein, 1941;Renyi, 1970].…”

Section: Nonlinear Model Based Data Analysismentioning

confidence: 99%

Nonlinear Methods of Cardiovascular Physics and Their Clinical Applicability

Wessel

Malberg²,

Bauernschmitt

et al. 2007

Int. J. Bifurcation Chaos

102

107

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In this tutorial we present recently developed nonlinear methods of cardiovascular physics and show their potentials to clinically relevant problems in cardiology. The first part describes methods of cardiovascular physics, especially data analysis and modeling of noninvasively measured biosignals, with the aim to improve clinical diagnostics and to improve the understanding of cardiovascular regulation. Applications of nonlinear data analysis and modeling tools are various and outlined in the second part of this tutorial: monitoring-, diagnosis-, course and mortality prognoses as well as early detection of heart diseases. We show, that these data analyses and modeling methods lead to significant improvements in different medical fields.Keywords: Cardiovascular physics; nonlinear data analysis and modeling; heart rate and blood pressure variability; baroreflex sensitivity. List of Abbreviations

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A Connection between Correlation and Contingency

Cited by 460 publications

References 0 publications

Four simple axioms of dependence measures

Four simple axioms of dependence measures

Two-stage least squares and indirect least squares algorithms for simultaneous equations models

Nonlinear Methods of Cardiovascular Physics and Their Clinical Applicability

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