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A denormalized U-statistic which cannot be decoupled from some associated stopping times

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Abstract

Let X1,X2,... be i.i.d. mean zero random variables and Sn=X1+...+Xn. For any stopping time T w.r.t. {Xn} let denote a copy of T which is independent of {Xn}. We exhibit a family of distributions and stopping times T such that and yet Emax1

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