Calibrating Dependence Between Random Elements

Abram M. Kagan () and Gábor J. Székely ()
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Abram M. Kagan: University of Maryland
Gábor J. Székely: National Science Foundation

Journal of Theoretical Probability, 2021, vol. 34, issue 2, 784-790

Abstract: Abstract Attempts to quantify dependence between random elements X and Y via maximal correlation go back to Gebelein (Z Angew Math Mech 21:364–379, 1941) and Rényi (Acta Math Acad Sci 10:441–451, 1959). After summarizing properties (including some new) of the Rényi measure of dependence, a calibrated scale of dependence is introduced. It is based on the “complexity” of approximating functions of X by functions of Y.

Keywords: Quantification; Measures of dependence; Projection; Primary 60H99; Secondary 62E10 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-020-00995-1

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