%0 Journal Article
%@ 0167-7152
%A Dümbgen, Lutz
%D 1998
%F heidok:21960
%J Statistics & Probability Letters
%K Exponential Inequality, Linear Rank Statistic, Permutation Bridge, Random Permutation
%N 4
%P 355-361
%R 10.11588/heidok.00021960
%T Symmetrization and Decoupling of Combinatorial Random Elements
%U https://archiv.ub.uni-heidelberg.de/volltextserver/21960/
%V 39
%X Let Φ = (φij)1 ⩽ij⩽n be a random matrix whose components φij are independent stochastic processes on some index set T. Let S = ∑i=1nφiπ(i), where Π is a random permutation of {1,2, …, n}, independent from Φ. This random element is compared with its symmetrized version S0 := ∑i=1n ξiφiπ(i) and its decoupled version S := ∑i=1n φiπ(i), where ξ = (ξi)1 ⩽i⩽n is a Rademacher sequence and Π is uniformly distributed on {1,2,…,n}n such that Φ, Π, Π and ξ are independent. It is shown that for a broad class of convex functions Ψ on RT the following symmetrization and decoupling inequalities hold: EΨ(S−ES) ⩽ Ψ(kS0)EΨ(γ(S−ES)) where κ, γ > 0 are universal constants.