Hoeffding’s Inequality for Sums of Dependent Random Variables

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F17%3A00483677" target="_blank" >RIV/67985807:_____/17:00483677 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00009-017-1043-2" target="_blank" >http://dx.doi.org/10.1007/s00009-017-1043-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00009-017-1043-2" target="_blank" >10.1007/s00009-017-1043-2</a>

Result language
angličtina
Original language name
Hoeffding’s Inequality for Sums of Dependent Random Variables
Original language description
Let X 1 , … , X n be, possibly dependent, [0, 1]-valued random variables. What is a sharp upper bound on the probability that their sum is significantly larger than their mean? In the case of independent random variables, a fundamental tool for bounding such probabilities is devised by Wassily Hoeffding. In this paper, we provide a generalisation of Hoeffding’s theorem. We obtain an estimate on the aforementioned probability that is described in terms of the expectation, with respect to convex functions, of a random variable that concentrates mass on the set { 0 , 1 , … , n}. Our main result yields concentration inequalities for several sums of dependent random variables such as sums of martingale difference sequences, sums of k-wise independent random variables, as well as for sums of arbitrary [0, 1]valued random variables.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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