On Measures of Average Quadrant Dependence

Let be a joint distribution function of a pair (, ) of continuous random variables with marginal distribution functions and , respectively. It is known that the expression (, ) − ()() measures “local” quadrant dependence at each point (, ) in ℝ. In this paper we study measures of association that can be constructed based on average quadrant dependence, i.e., the expectation with respect to another joint distribution function ′—with margins and —of the one-dimensional random variables (, ) − ()() and |(, ) − ()()|. The construction examined here includes some well-known measures of association