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Introduction

Stéphane Boucheron, Gábor Lugosi, and Pascal Massart

in Concentration Inequalities: A Nonasymptotic Theory of Independence

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199535255
eISBN:
9780191747106
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535255.003.0001
Subject:
Mathematics, Probability / Statistics, Applied Mathematics

In this introductory chapter we briefly review the history of the subject and outline the contents, as an appetizer for the rest of the book.


Concentration and Isoperimetry

Stéphane Boucheron, Gábor Lugosi, and Pascal Massart

in Concentration Inequalities: A Nonasymptotic Theory of Independence

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199535255
eISBN:
9780191747106
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535255.003.0007
Subject:
Mathematics, Probability / Statistics, Applied Mathematics

In this chapter we discuss some aspects of the rich relationship between isoperimetric problems and concentration inequalities. We establish a connection between isoperimetric inequalities in general ... More


Concentration Inequalities: A Nonasymptotic Theory of Independence

Stéphane Boucheron, Gábor Lugosi, and Pascal Massart

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199535255
eISBN:
9780191747106
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535255.001.0001
Subject:
Mathematics, Probability / Statistics, Applied Mathematics

This monograph presents a mathematical theory of concentration inequalities for functions of independent random variables. The basic phenomenon under investigation is that if a function of many ... More


Basic Inequalities

Stéphane Boucheron, Gábor Lugosi, and Pascal Massart

in Concentration Inequalities: A Nonasymptotic Theory of Independence

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199535255
eISBN:
9780191747106
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535255.003.0002
Subject:
Mathematics, Probability / Statistics, Applied Mathematics

In this chapter we first review some elementary facts about tail probabilities. Then, we describe the so-called Cramér–Chernoff method. We single out two types of tail behaviors, sub-Gaussian and ... More


How Concentrated Are Ethnic Groups in Schools?

Richard Harris and Ron Johnston

in Ethnic Segregation Between Schools: Is It Increasing or Decreasing in England?

Published in print:
2020
Published Online:
January 2021
ISBN:
9781529204780
eISBN:
9781529204889
Item type:
chapter
Publisher:
Policy Press
DOI:
10.1332/policypress/9781529204780.003.0004
Subject:
Education, Educational Policy and Politics

The Casey Review cites a study by the think-tank Demos that shows the majority of ethnic minority students attend schools where ‘minority’ groups are in the majority. That statistic is correct but ... More


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