Almost opposite regression dependence in bivariate distributions
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Date
2014-08-08
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Abstract
Let X,Y be two continuous random variables. Investigating the regression
dependence of Y on X, respectively, of X on Y, we show that the two of
them can have almost opposite behavior. Indeed, given any e > 0, we construct
a bivariate random vector (X,Y) such that the respective regression
dependence measures r2|1(X,Y), r1|2(X,Y) ∈ [0,1] introduced in Dette et al.
(2013) satisfy r2|1(X,Y) = 1 as well as r1|2(X,Y) <e .
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Keywords
regression