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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Major, Peter¹ 

[1] Hungarian Acad Sci, Alfred Renyi Inst Math, H-1051 Budapest, Hungary

关键词: Uniform covering numbers;    Classes of functions with polynomially increasing covering numbers;    Vapnik-Cervonenlds classes;    Hoeffding inequality;   

DOI  :  10.1016/j.spa.2015.07.016

来源: Elsevier

【 摘 要 】

We take a class of functions F with polynomial covering numbers on a measurable space (X, chi) together with a sequence of independent, identically distributed X-space valued random variables xi(1), ..., xi(n), 62, and give a good estimate on the tail distribution of sup(f is an element of F) Sigma(n)(j=1) f(xi(j)) if the expected values E vertical bar f(xi 1)vertical bar are very small for all f is an element of 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. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

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