Almost opposite regression dependence in bivariate distributions

Karl Siburg () and Pavel Stoimenov ()

Statistical Papers, 2015, vol. 56, issue 4, 1033-1039

Abstract: Let $$X$$ X , $$Y$$ Y be two continuous random variables. Investigating the regression dependence of $$Y$$ Y on $$X$$ X , respectively, of $$X$$ X on $$Y$$ Y , we show that the two of them can have almost opposite behavior. Indeed, given any $$\epsilon >0$$ ϵ > 0 , we construct a bivariate random vector $$(X,Y)$$ ( X , Y ) such that the respective regression dependence measures $$r_{2|1}(X,Y), r_{1|2}(X,Y) \in [0,1]$$ r 2 | 1 ( X , Y ) , r 1 | 2 ( X , Y ) ∈ [ 0 , 1 ] introduced in Dette et al. (Scand. J. Stat. 40(1):21–41, 2013 ) satisfy $$r_{2|1}(X,Y)=1$$ r 2 | 1 ( X , Y ) = 1 as well as $$r_{1|2}(X,Y) > \epsilon $$ r 1 | 2 ( X , Y ) > ϵ . Copyright Springer-Verlag Berlin Heidelberg 2015

Keywords: Regression; Measure of regression dependence; Copula (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s00362-014-0622-6

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