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Sharp estimate on the supremum of a class of sums of small i.i.d. random variables

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  • Major, Péter

Abstract

We take a class of functions F with polynomial covering numbers on a measurable space (X,X) together with a sequence of independent, identically distributed X-space valued random variables ξ1,…,ξn, and give a good estimate on the tail distribution of supf∈F∑j=1nf(ξj) if the expected values E|f(ξ1)| are very small for all f∈F. In a subsequent paper (Major, in press) we give a sharp bound for the supremum of normalized sums of i.i.d. random variables in a more general case. But the proof of that estimate is based on the results in this work.

Suggested Citation

  • Major, Péter, 2016. "Sharp estimate on the supremum of a class of sums of small i.i.d. random variables," Stochastic Processes and their Applications, Elsevier, vol. 126(1), pages 100-117.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:1:p:100-117
    DOI: 10.1016/j.spa.2015.07.016
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