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Symmetrization and Decoupling of Combinatorial Random Elements

Dümbgen, Lutz

In: Statistics & Probability Letters, 39 (1998), Nr. 4. pp. 355-361. ISSN 0167-7152

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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.

Item Type: Article
Journal or Publication Title: Statistics & Probability Letters
Volume: 39
Number: 4
Date Deposited: 09 Oct 2016 16:27
Date: 1998
ISSN: 0167-7152
Page Range: pp. 355-361
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 310 General statistics
Uncontrolled Keywords: Exponential Inequality, Linear Rank Statistic, Permutation Bridge, Random Permutation
Schriftenreihe ID: Beiträge zur Statistik > Reports
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