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A Copula‐Based Non‐parametric Measure of Regression Dependence
Author(s) -
DETTE HOLGER,
SIBURG KARL F.,
STOIMENOV PAVEL A.
Publication year - 2013
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2011.00767.x
Subject(s) - mathematics , copula (linguistics) , bivariate analysis , estimator , parametric statistics , measure (data warehouse) , statistics , univariate , monotone polygon , regression , regression analysis , tail dependence , econometrics , multivariate statistics , geometry , database , computer science
. This article presents a framework for comparing bivariate distributions according to their degree of regression dependence. We introduce the general concept of a regression dependence order (RDO). In addition, we define a new non‐parametric measure of regression dependence and study its properties. Besides being monotone in the new RDOs, the measure takes on its extreme values precisely at independence and almost sure functional dependence, respectively. A consistent non‐parametric estimator of the new measure is constructed and its asymptotic properties are investigated. Finally, the finite sample properties of the estimate are studied by means of a small simulation study.