Calibrating Dependence Between Random Elements

Calibrating Dependence Between Random Elements

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...

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Veröffentlicht in:Journal of theoretical probability 2021-06, Vol.34 (2), p.784-790
Hauptverfasser: Kagan, Abram M., Székely, Gábor J.
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Statistics
Yttrium
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Zusammenfassung: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 .
ISSN:0894-9840
1572-9230
DOI:10.1007/s10959-020-00995-1