Hoeffding’s Inequality for Sums of Dependent Random Variables

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Hoeffding’s Inequality for Sums of Dependent Random Variables

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Hoeffding’s Inequality for Sums of Dependent Random Variables

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mediterranean Journal of Mathematics

ISSN

1660-5446

e-ISSN

—

Svazek periodika

14

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

16

Strana od-do

—

Kód UT WoS článku

000417856400003

EID výsledku v databázi Scopus

2-s2.0-85037039956