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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


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