Symmetrization and decoupling of combinatorial random elements

Lutz Duembgen

Statistics & Probability Letters, 1998, vol. 39, issue 4, 355-361

Abstract: Let [Phi] = ([phi]ij)1 [less-than-or-equals, slant]ij[less-than-or-equals, slant]n be a random matrix whose components [phi]ij are independent stochastic processes on some index set . Let , where [Pi] is a random permutation of {1,2, ..., n}, independent from [Phi]. This random element is compared with its symmetrized version and its decoupled version , where [xi] = ([xi]i)1 [less-than-or-equals, slant]i[less-than-or-equals, slant]n is a Rademacher sequence and is uniformly distributed on {1,2,...,n}n such that [Phi], [Pi], and [xi] are independent. It is shown that for a broad class of convex functions [Psi] on R the following symmetrization and decoupling inequalities hold: where ?, [gamma] > 0 are universal constants.

Keywords: Exponential; inequality; Linear; rank; statistic; Permutation; bridge; Random; permutation (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (1)

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