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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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