## Asymptotic Properties of the Estimators

*Søren Johansen*

### in Likelihood-Based Inference in Cointegrated Vector Autoregressive Models

- Published in print:
- 1995
- Published Online:
- November 2003
- ISBN:
- 9780198774501
- eISBN:
- 9780191596476
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198774508.003.0013
- Subject:
- Economics and Finance, Econometrics

The asymptotic properties of the estimators for adjustment coefficients and cointegrating relations are derived under the assumption that they have been estimated unrestrictedly. We show that the ... More

## Phase Transitions and Renormalization Group

*Jean Zinn-Justin*

- Published in print:
- 2007
- Published Online:
- January 2010
- ISBN:
- 9780199227198
- eISBN:
- 9780191711107
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199227198.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This book provides an elementary introduction to the notions of continuum limit and universality in statistical systems with a large number of degrees of freedom. The existence of a continuum limit ... More

## Likelihoods and likelihood ratios

*Thomas D. Wickens*

### in Elementary Signal Detection Theory

- Published in print:
- 2001
- Published Online:
- April 2010
- ISBN:
- 9780195092509
- eISBN:
- 9780199893812
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195092509.003.0009
- Subject:
- Psychology, Cognitive Psychology

Likelihoods — the probabilities treated as a function of their parameters — are a key concept in statistical decision theory. When applied to signal detection, they give a general method for ... More

## Entropy and Mutual Information

*Partha P. Mitra and Hemant Bokil*

### in Observed Brain Dynamics

- Published in print:
- 2007
- Published Online:
- May 2009
- ISBN:
- 9780195178081
- eISBN:
- 9780199864829
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195178081.003.0014
- Subject:
- Neuroscience, Techniques, Molecular and Cellular Systems

In the neuroscience literature, significant use has been made of entropy as a measure of variability, and mutual information as a measure of association. Part of the attraction of these measures ... More

## Random Variables

*James Davidson*

### in Stochastic Limit Theory: An Introduction for Econometricians

- Published in print:
- 1994
- Published Online:
- November 2003
- ISBN:
- 9780198774037
- eISBN:
- 9780191596117
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198774036.003.0008
- Subject:
- Economics and Finance, Econometrics

Specializing the concepts of Ch. 7 to the case of real variables, this chapter introduces distribution functions, discrete and continuous distributions, and describes examples such as the binomial, ... More

## Dimensionality and Its Reduction

*Andrew J. Connolly, Jacob T. VanderPlas, Alexander Gray, Andrew J. Connolly, Jacob T. VanderPlas, and Alexander Gray*

### in Statistics, Data Mining, and Machine Learning in Astronomy: A Practical Python Guide for the Analysis of Survey Data

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691151687
- eISBN:
- 9781400848911
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691151687.003.0007
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

With the dramatic increase in data available from a new generation of astronomical telescopes and instruments, many analyses must address the question of the complexity as well as size of the data ... More

## Some Extensions

*James Davidson*

### in Stochastic Limit Theory: An Introduction for Econometricians

- Published in print:
- 1994
- Published Online:
- November 2003
- ISBN:
- 9780198774037
- eISBN:
- 9780191596117
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198774036.003.0025
- Subject:
- Economics and Finance, Econometrics

Four extensions of the CLT are considered in this chapter. First, estimated normalization, using methods of heteroscedasticity and autocorrelation consistent variance estimation. Second, random ... More

## Power Laws and Long Tails

*David P. Feldman*

### in Chaos and Fractals: An Elementary Introduction

- Published in print:
- 2012
- Published Online:
- December 2013
- ISBN:
- 9780199566433
- eISBN:
- 9780191774966
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199566433.003.0021
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter examines distributions known as power laws, which are fractal because they are scale-free. It first considers normal or Gaussian distributions to provide a useful contrast to power-law ... More

## Asset fluctuations and scaling

*Peter Richmond, Jürgen Mimkes, and Stefan Hutzler*

### in Econophysics and Physical Economics

- Published in print:
- 2013
- Published Online:
- December 2013
- ISBN:
- 9780199674701
- eISBN:
- 9780191780066
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199674701.003.0009
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter first discusses the notion of stable distributions and shows that the consequence of this assumption is that the characteristic function of the corresponding distribution function has a ... More

## Asymmetric Dependence Patterns in Financial Returns: An Empirical Investigation Using Local Gaussian Correlation

*Bård Støve and Dag Tjøstheim*

### in Essays in Nonlinear Time Series Econometrics

- Published in print:
- 2014
- Published Online:
- August 2014
- ISBN:
- 9780199679959
- eISBN:
- 9780191760136
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199679959.003.0013
- Subject:
- Economics and Finance, Econometrics

A number of studies have provided evidence that financial returns exhibit asymmetric dependence, such as increased dependence during bear markets, but there seems to be no agreement as to how such ... More

## The random walk: Universality and continuum limit

*Jean Zinn-Justin*

### in From Random Walks to Random Matrices

- Published in print:
- 2019
- Published Online:
- August 2019
- ISBN:
- 9780198787754
- eISBN:
- 9780191829840
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198787754.003.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The first chapter discusses the asymptotic properties at large time and space of the familiar example of the random walk. The universality of a large scale behaviour and, correspondingly, the ... More

## The universality theorem

*Razvan Gurau*

### in Random Tensors

- Published in print:
- 2016
- Published Online:
- January 2017
- ISBN:
- 9780198787938
- eISBN:
- 9780191829918
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198787938.003.0006
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Particle Physics / Astrophysics / Cosmology

This chapter initiates the study of random tensors and presents a universality theorem. It first introduces the Gaussian distribution for random tensors and then proceeds to the study of general ... More

## Entropy: science (and some history)

*Robert T. Hanlon*

### in Block by Block: The Historical and Theoretical Foundations of Thermodynamics

- Published in print:
- 2020
- Published Online:
- April 2020
- ISBN:
- 9780198851547
- eISBN:
- 9780191886133
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198851547.003.0024
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Entropy is a natural consequence of our discrete world involving large systems of colliding particles, atoms, and molecules. Entropy is quantified based on the number of different ways that such ... More

## Maxwell: the rise of statistical mechanics

*Robert T. Hanlon*

### in Block by Block: The Historical and Theoretical Foundations of Thermodynamics

- Published in print:
- 2020
- Published Online:
- April 2020
- ISBN:
- 9780198851547
- eISBN:
- 9780191886133
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198851547.003.0041
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Maxwell produced two publications on the kinetic theory of gases in which he proposed his eponymous velocity distribution of velocities, his theory on the equipartition of energy, and finally his ... More

## Econophysics and Financial Economics: An Emerging Dialogue

*Franck Jovanovic and Christophe Schinckus*

- Published in print:
- 2017
- Published Online:
- December 2016
- ISBN:
- 9780190205034
- eISBN:
- 9780190205065
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780190205034.001.0001
- Subject:
- Economics and Finance, Financial Economics

How can we create a profitable dialogue between financial economists and econophysicists? This book moves beyond the disciplinary frontiers in order to initiate the development of a common ... More

## Markov Processes and Random Sampling

*Ulf Grenander and Michael I. Miller*

### in Pattern Theory: From representation to inference

- Published in print:
- 2006
- Published Online:
- November 2020
- ISBN:
- 9780198505709
- eISBN:
- 9780191916564
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198505709.003.0019
- Subject:
- Computer Science, Programming Languages

The parameter spaces of natural patterns are so complex that inference must often proceed compositionally, successively building up more and more complex structures, ... More

## Introduction To Stochastic Processes

*Abraham Nitzan*

### in Chemical Dynamics in Condensed Phases: Relaxation, Transfer and Reactions in Condensed Molecular Systems

- Published in print:
- 2006
- Published Online:
- November 2020
- ISBN:
- 9780198529798
- eISBN:
- 9780191916649
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198529798.003.0013
- Subject:
- Chemistry, Physical Chemistry

As discussed in Section 1.5, the characterization of observables as random variables is ubiquitous in descriptions of physical phenomena. This is not ... More

## Concepts of Evolutionary Modeling and Evolutionary Algorithms

*Roman M. Krzanowski and Jonathan Raper*

### in Spatial Evolutionary Modeling

- Published in print:
- 2001
- Published Online:
- November 2020
- ISBN:
- 9780195135688
- eISBN:
- 9780197561621
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195135688.003.0008
- Subject:
- Computer Science, Mathematical Theory of Computation

This book is about evolutionary algorithms as applied to spatial and geographic phenomena. Why are we writing this book? Do these new algorithms deliver ... More

## Preparation, Analysis, and Degradation

*James E. Mark, Dale W. Schaefer, and Gui Lin*

### in Title Pages

- Published in print:
- 2015
- Published Online:
- November 2020
- ISBN:
- 9780195181739
- eISBN:
- 9780197562321
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195181739.003.0004
- Subject:
- Chemistry, Polymer Chemistry

Elemental silicon on which the entire technology is based is typically obtained by reduction of the mineral silica with carbon at high temperatures: . . . SiO2 + 2C → ... More

## General Properties

*James E. Mark, Dale W. Schaefer, and Gui Lin*

### in The Polysiloxanes

- Published in print:
- 2015
- Published Online:
- November 2020
- ISBN:
- 9780195181739
- eISBN:
- 9780197562321
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195181739.003.0007
- Subject:
- Chemistry, Polymer Chemistry

Many of the properties of the polysiloxanes have been tabulated in handbooks of polymer science and engineering. Recent work has included the stretching of ... More