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Estimating functions

Christopher G. Small and Jinfang Wang

in Numerical Methods for Nonlinear Estimating Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506881
eISBN:
9780191709258
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506881.003.0002
Subject:
Mathematics, Probability / Statistics

This chapter gives a survey of the basic concepts of estimating functions, which are used in subsequent chapters. The concept of unbiasedness for estimating functions is introduced as a ... More


Hertz on the Hamilton formalism

JESPER LÜTZEN

in Mechanistic Images in Geometric Form: Heinrich Hertz's 'Principles of Mechanics'

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567370
eISBN:
9780191717925
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567370.003.0023
Subject:
Physics, History of Physics

In the introduction to his book Principles of Mechanics, Heinrich Hertz emphasised that one of the advantages of his geometric formulation of his mechanics is that it throws a bright light upon ... More


Quantum Statistics of Fields

STEPHEN M. BARNETT and PAUL M. RADMORE

in Methods in Theoretical Quantum Optics

Published in print:
2002
Published Online:
February 2010
ISBN:
9780198563617
eISBN:
9780191714245
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198563617.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter considers methods for describing the quantum statistics of a single mode of the electromagnetic field. Some of these methods may be extended to multimode fields, and this is discussed in ... More


Characteristic Functions

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:
10.1093/0198774036.003.0011
Subject:
Economics and Finance, Econometrics

This chapter begins with a look at convolutions and the distribution of sums of random variables. It briefly surveys complex number theory before defining the characteristic function and studying its ... More


Review of probability

Melvin Lax, Wei Cai, and Min Xu

in Random Processes in Physics and Finance

Published in print:
2006
Published Online:
January 2010
ISBN:
9780198567769
eISBN:
9780191718359
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567769.003.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter reviews probability theory, limiting the discussion to the study of random events as opposed to random processes, the latter being a sequence of random events extended over a period of ... More


Weak Convergence of Distributions

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:
10.1093/0198774036.003.0022
Subject:
Economics and Finance, Econometrics

This chapter introduces the fundamentals of weak convergence for real sequences. Definitions and examples are given. The Skorokhod representation theorem is proved, and the chapter then considers the ... More


PROBABILITY THEORY

Robert M. Mazo

in Brownian Motion: Fluctuations, Dynamics, and Applications

Published in print:
2008
Published Online:
January 2010
ISBN:
9780199556441
eISBN:
9780191705625
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199556441.003.0002
Subject:
Physics, Condensed Matter Physics / Materials

This chapter begins with a review of elementary probability theory, conditional probability, and statistical independence. It explains the notion of a random variable and its distribution function or ... More


Acts of Mathematical Creation

Paul Erickson

in The World the Game theorists Made

Published in print:
2015
Published Online:
May 2016
ISBN:
9780226097039
eISBN:
9780226097206
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226097206.003.0002
Subject:
History, History of Science, Technology, and Medicine

Despite the ex post facto identification of a number of “anticipations” of game-theoretic results through history, it is generally agreed that modern game theory’s founding work was mathematician ... More


Blocking

Debraj Ray

in A Game-Theoretic Perspective on Coalition Formation

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199207954
eISBN:
9780191709104
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199207954.003.0011
Subject:
Economics and Finance, Financial Economics

This chapter begins a second approach to coalition formation, one firmly grounded in coalitions as fundamental behavioral units. A central notion is that of blocking and the attendant concepts that ... More


Clarification and defence

John Collins

in The Unity of Linguistic Meaning

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199694846
eISBN:
9780191732027
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199694846.003.0006
Subject:
Philosophy, Philosophy of Language, Philosophy of Mind

There are three strands of justification for the account of combinatorial unity presented in the last chapter. The first is negative: the other extant accounts of unity are, I have argued, either ... More


Phase Space Distributions

Bryan J. Dalton, John Jeffers, and Stephen M. Barnett

in Phase Space Methods for Degenerate Quantum Gases

Published in print:
2014
Published Online:
April 2015
ISBN:
9780199562749
eISBN:
9780191747311
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199562749.003.0007
Subject:
Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

This chapter formally presents the representation of the quantum density operator by phase space distribution functions of phase space variables, leading to expressions for quantum correlation ... More


Characteristic functions

J. Klafter and I.M. Sokolov

in First Steps in Random Walks: From Tools to Applications

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199234868
eISBN:
9780191775024
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199234868.003.0001
Subject:
Physics, Soft Matter / Biological Physics

Since simple random walk is a process with independent increments, its properties are represented in the most simple way by using the techniques based on characteristic functions. This chapter ... More


Langevin processes

Melvin Lax, Wei Cai, and Min Xu

in Random Processes in Physics and Finance

Published in print:
2006
Published Online:
January 2010
ISBN:
9780198567769
eISBN:
9780191718359
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567769.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Just as Fokker–Planck processes are a generalisation of thermal noise, Langevin processes constitute a generalisation of shot noise. In general, Langevin processes permit a larger class of problems ... More


The method of joint probability distribution functions, neighbourhoods, and representations

Carmelo Giacovazzo

in Phasing in Crystallography: A Modern Perspective

Published in print:
2013
Published Online:
November 2020
ISBN:
9780199686995
eISBN:
9780191918377
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199686995.003.0009
Subject:
Chemistry, Crystallography: Chemistry

Wilson statistics, described in Chapter 2, aims at calculating the distribution of the structure factor P(F) ≡ P(|F|, φ) when nothing is known about the structure; the ... More


Canonical & Gauge Transformations

Peter Mann

in Lagrangian and Hamiltonian Dynamics

Published in print:
2018
Published Online:
August 2018
ISBN:
9780198822370
eISBN:
9780191861253
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198822370.003.0018
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In this chapter, the Hamilton–Jacobi formulation is discussed in two parts: from a generating function perspective and as a variational principle. The Poincaré–Cartan 1-form is derived and solutions ... More


Estimation Bounds for Automated Object Recognition

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/9780198505709.003.0014
Subject:
Computer Science, Programming Languages

Thus far we have only studied representations of the source. Now we add the channel, pushing us into the frameworks of estimate then examine estimation bounds for ... More


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