KIT | KIT-Bibliothek | Impressum | Datenschutz

Lancaster correlation: A new dependence measure linked to maximum correlation

Holzmann, Hajo; Klar, Bernhard ORCID iD icon 1
1 Institut für Stochastik (STOCH), Karlsruher Institut für Technologie (KIT)

Abstract:

We suggest novel correlation coefficients which equal the maximum correlation for a class of bivariate Lancaster distributions while being only slightly smaller than maximum correlation for a variety of further bivariate distributions. In contrast to maximum correlation, however, our correlation coefficients allow for rank and moment-based estimators which are simple to compute and have tractable asymptotic distributions. Confidence intervals resulting from these asymptotic approximations and the covariance bootstrap show good finite-sample coverage. In a simulation, the power of asymptotic as well as permutation tests for independence based on our correlation measures compares favorably with competing methods based on distance correlation or rank coefficients for functional dependence, among others. Moreover, for the bivariate normal distribution, our correlation coefficients equal the absolute value of the Pearson correlation, an attractive feature for practitioners which is not shared by various competitors. We illustrate the practical usefulness of our methods in applications to two real data sets.


Verlagsausgabe §
DOI: 10.5445/IR/1000172416
Veröffentlicht am 18.07.2024
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2024
Sprache Englisch
Identifikator ISSN: 0303-6898, 1467-9469
KITopen-ID: 1000172416
Erschienen in Scandinavian Journal of Statistics
Verlag John Wiley and Sons
Vorab online veröffentlicht am 03.07.2024
Schlagwörter correlation coefficient, independence tests, Lancaster distribution, rank statistics
Nachgewiesen in Dimensions
Web of Science
Scopus
Relationen in KITopen
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
KITopen Landing Page