eprintid: 21960
rev_number: 15
eprint_status: archive
userid: 466
dir: disk0/00/02/19/60
datestamp: 2016-10-09 16:27:37
lastmod: 2016-11-15 09:47:27
status_changed: 2016-10-09 16:27:37
type: article
metadata_visibility: show
creators_name: Dümbgen, Lutz
title: Symmetrization and Decoupling of Combinatorial Random Elements
subjects: ddc-310
divisions: i-110400
keywords: Exponential Inequality, Linear Rank Statistic, Permutation Bridge, Random Permutation
abstract: 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
id_scheme: DOI
id_number: 10.11588/heidok.00021960
schriftenreihe_cluster_id: sr-10b
schriftenreihe_order: 12
ppn_swb: 1658989546
own_urn: urn:nbn:de:bsz:16-heidok-219605
language: eng
bibsort: DUMBGENLUTSYMMETRIZA1998
full_text_status: public
publication: Statistics & Probability Letters
volume: 39
number: 4
pagerange: 355-361
issn: 0167-7152
citation:   Dümbgen, Lutz  (1998) Symmetrization and Decoupling of Combinatorial Random Elements.  Statistics & Probability Letters, 39 (4).  pp. 355-361.  ISSN 0167-7152     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/21960/1/report.12%281%29.pdf