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TYPICAL VERTEX DEGREES

Mathew Penrose

in Random Geometric Graphs

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506263
eISBN:
9780191707858
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506263.003.0004
Subject:
Mathematics, Probability / Statistics

This chapter is concerned with the empirical process of k-nearest neighbour distances for n random points, where k=k(n) is specified and is either fixed or grows with n. That is, the proportion of ... More


An Analysis of the Indicator Saturation Estimator as a Robust Regression Estimator *

Søren Johansen and Bent Nielsen

in The Methodology and Practice of Econometrics: A Festschrift in Honour of David F. Hendry

Published in print:
2009
Published Online:
September 2009
ISBN:
9780199237197
eISBN:
9780191717314
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199237197.003.0001
Subject:
Economics and Finance, Econometrics

This chapter analyzes an algorithm suggested by Hendry (1999) for estimation in a regression with more regressors than observations, with the purpose of finding an estimator that is robust to ... More


The Expected Value of Suprema of Empirical Processes

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/9780199535255.003.0013
Subject:
Mathematics, Probability / Statistics, Applied Mathematics

Bounding the expected value of the supremum of an empirical process is a central object of the study of empirical processes and the purpose of this chapter is to present elements of this rich theory. ... More


The Variance of Suprema of Empirical Processes

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/9780199535255.003.0011
Subject:
Mathematics, Probability / Statistics, Applied Mathematics

In this chapter we focus our attention on the variance of the supremum of an empirical process. In this relatively simple, problem, we gain insight into some of the principal phenomena in a ... More


Suprema of Empirical Processes: Exponential 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/9780199535255.003.0012
Subject:
Mathematics, Probability / Statistics, Applied Mathematics

In this chapter we continue the study of suprema of empirical processes started in Chapter 11 and we prove exponential concentration inequalities. Our main tool is the entropy method introduced in ... 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


Functional Central Limit Theorem for Empirical Processes

Florence Merlevède, Magda Peligrad, and Sergey Utev

in Functional Gaussian Approximation for Dependent Structures

Published in print:
2019
Published Online:
April 2019
ISBN:
9780198826941
eISBN:
9780191865961
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198826941.003.0015
Subject:
Mathematics, Probability / Statistics

Here we discuss the Gaussian approximation for the empirical process under different kinds of dependence assumptions for the underlying stationary sequence. First, we state a general criterion to ... More


Six Myths about Schizophrenia: A Paradigm Well Beyond Its Use-By Date?

Richard P. Bentall

in Extraordinary Science and Psychiatry: Responses to the Crisis in Mental Health Research

Published in print:
2017
Published Online:
September 2017
ISBN:
9780262035484
eISBN:
9780262341752
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262035484.003.0010
Subject:
Psychology, Clinical Psychology

The target of this chapter is a set of six commonly held assumptions in the biomedical approach to schizophrenia, a highly regarded view in mainstream American psychiatry. A careful examination of ... More


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