title: Symmetrization and Decoupling of Combinatorial Random Elements
creator: Dümbgen, Lutz
subject: ddc-310
subject: 310 General statistics
description: 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.
date: 1998
type: Article
type: info:eu-repo/semantics/article
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/21960/1/report.12%281%29.pdf
identifier: DOI:10.11588/heidok.00021960
identifier: urn:nbn:de:bsz:16-heidok-219605
identifier:   Dümbgen, Lutz  (1998) Symmetrization and Decoupling of Combinatorial Random Elements.  Statistics & Probability Letters, 39 (4).  pp. 355-361.  ISSN 0167-7152     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/21960/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng