Aspects of Negative Dependence Structures
In this article, several counterexamples are provided which show that some concepts of negative dependence are strictly stronger than others. An open problem is solved which was posed by Hu et al. (2005) and refers to whether strong negative orthant dependence implies the negative superadditive dependence. Finally, for a dependence random vector (X 1, X 2,…, X n ) (n ≥ 2), we construct uncorrelated random variables Y i = X i + cU i , a.e. i = 1, 2,…, n under certain dependence structures, where the vector U = (U 1, U 2,…, U n ) is independent of (X 1, X 2,…, X n ).