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Symmetrization and decoupling of combinatorial random elements

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  • Duembgen, Lutz

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.

Suggested Citation

  • Duembgen, Lutz, 1998. "Symmetrization and decoupling of combinatorial random elements," Statistics & Probability Letters, Elsevier, vol. 39(4), pages 355-361, August.
    • Handle: RePEc:eee:stapro:v:39:y:1998:i:4:p:355-361
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    Cited by:

    1. Horváth, Lajos & Shao, Qi-Man, 2007. "Limit theorems for permutations of empirical processes with applications to change point analysis," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1870-1888, December.

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