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We introduce the concept of monotone dependence function of bivariate distributions without moment conditions. Our concept gives, among other things, a characterization of independent and positively (negatively) quadrant dependent random variables.
The notion of g-monotone dependence function introduced in [4] generalizes the notions of the monotone dependence function and the quantile monotone dependence function defined in [2], [3] and [6]. In this paper we study the asymptotic behaviour of sample g-monotone dependence functions and their strong properties.
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