A Copula‐Based Non‐parametric Measure of Regression Dependence. (20th February 2012)

• Record Type: Journal Article
• Authors: DETTE, HOLGER; SIBURG, KARL F.; STOIMENOV, PAVEL A.
• Is Part Of: Scandinavian journal of statistics. Volume 40:Number 1(2013:Mar.)
• Page Start: 21
• Page End: 41
• Publication Date: 2012-02-20
• Subjects: Statistics -- Periodicals; 310
• DOI: 10.1111/j.1467-9469.2011.00767.x
• Languages: English
• ISSNs: 0303-6898

Abstract

<abstract abstract-type="main" xml:lang="en"> <title> <x xml:space="preserve">Abstract</x> </title> <p> <bold>Abstract. </bold> 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.</p> </abstract>