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Sharp estimate on the supremum of a class of partial sums of small i.i.d. random variables
[article]

2014
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arXiv
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pre-print

We take an L_1-dense class of functions F on a measurable space (X, X) together with a sequence of independent, identically distributed X-space valued random variables ξ_1,...,ξ_n and give a good estimate on the tail distribution of _f∈ F∑_j=1^n f(ξ_j) if the expected values E|f(ξ_1)| are very small for all f∈ F. In a subsequent paper [2] we shall give a sharp bound for the supremum of normalized sums of i.i.d. random variables in a more general case. But that estimate is a consequence of the results in this work.

arXiv:1407.1224v1
fatcat:palzma2dfnbmpjlklvm3ee5tk4