Extreme Points of the Set of All 2xn Bivariate Positive Quadrant Dependent Distributions with Fixed Marginals and Some Applications

摘要

The set of all bivariate distributions with support contained in ((i.j); i = 1,2 and j = 1,2..., n) which are positive quadrant dependent is a convex set. In the paper, an algebraic method is presented for the enumeration of all extreme points of this convex set. Certain measures of dependence, including Kendall's tau, are shown to be affine functions on this convex set. This property of being affine helps us to evaluate the asymptotic power of tests based on these measures of dependence for testing the hypothesis of independence against strict positive quadrant dependence.