Title of article :
The complete mixability and convex minimization problems with monotone marginal densities
Author/Authors :
Wang، نويسنده , , Bin and Wang، نويسنده , , Ruodu، نويسنده ,
Issue Information :
دوفصلنامه با شماره پیاپی سال 2011
Abstract :
Following the results of Rüschendorf and Uckelmann (2002) [20], we introduce the completely mixable distributions on R and prove that the distributions with monotone density and moderate mean are completely mixable. Using this method, we solve the minimization problem min X i ∼ P E f ( X 1 + ⋯ + X n ) for convex functions f and marginal distributions P with monotone density. Our results also provide valuable implications in variance minimization, bounds for the sum of random variables and risk theory.
Keywords :
Optimal coupling , Complete mixability , Monotone densities , Variance minimization , Multivariate dependence
Journal title :
Journal of Multivariate Analysis
Journal title :
Journal of Multivariate Analysis