A Kolmogorov inequality for the sum of independent Bernoulli random variables with unequal means
type: Item
instance of: scholarly article
title: A Kolmogorov inequality for the sum of independent Bernoulli random variables with unequal means
zbMATH Open document ID: 0824.60023
DOI: 10.1016/0167-7152(94)00120-W
author: Danny W. Turner
author: Dean M. Young
author: John W. jun. Seaman
published in: Statistics \& Probability Letters
publication date: 1995-10-31T00:00:00Z
review text: Let \(\{X_ i\}\) be a sequence of independent Bernoulli random variables such that \(X_ i\) has parameter \(p_ i\) with \(0 \leq p_ i \leq 1\). Let \(\overline X_ k = (1/k) \sum_ 1^ k X_ i\) and let \(\overline p_ k = (1/k) \sum^ k_ 1 p_ i\). Then for any constant \(\varepsilon \geq 0\) and any number \(n \geq 0\), \(P(\sup_{k \geq n} (\overline X_ k - \overline p_ k) \geq \varepsilon) \leq e^{-2n \varepsilon^ 2}\). This is the extension of the Kolmogorov inequality announced in 1963 without proof.
reviewed by: Birutė Kryžienė
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60E15
zbMATH DE Number: 768772
zbMATH Keywords: maximal inequalities
zbMATH Keywords: large deviation probabilities
zbMATH Keywords: Kolmogorov inequality
MaRDI profile type: Publication
cites work: On a Kolmogorov Inequality
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cites work: Q5333652
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full work available at URL: 0167-7152(94)00120-w
OpenAlex ID: W2068823761
description: scientific article; zbMATH DE number 768772