The complete mixability and convex minimization problems with monotone marginal densities

JOURNAL OF MULTIVARIATE ANALYSIS

卷:102

Article

Wang, Bin²  Wang, Ruodu¹ 

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

[2] Peking Univ, Dept Math, Beijing 100871, Peoples R China

关键词: Complete mixability;    Variance minimization;    Multivariate dependence;    Monotone densities;    Optimal coupling;   

DOI  :  10.1016/j.jmva.2011.05.002

来源: Elsevier

【 摘 要 】

Following the results of Ruschendorf 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(xi similar to 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. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free