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

Péter Major

Stochastic Processes and their Applications, 2016, vol. 126, issue 1, 100-117

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.

Keywords: Uniform covering numbers; Classes of functions with polynomially increasing covering numbers; Vapnik–Červonenkis classes; Hoeffding inequality (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.spa.2015.07.016

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