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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


Weak Convergence in Metric Spaces

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:
10.1093/0198774036.003.0026
Subject:
Economics and Finance, Econometrics

This chapter lays the foundations for functional limit theory by considering the case of general metric spaces, from a topological standpoint. It develops tools to replace the method of ... More


Cadlag 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:
10.1093/0198774036.003.0028
Subject:
Economics and Finance, Econometrics

This chapter considers the space D, of functions on the unit interval that are continuous on the right with left limits. D contains and extends the space C, but is nonseparable, so to work with it ... More


Graph-Theoretic and Linear Algebra Formulations

Guillaume Fertin, Anthony Labarre, Irena Rusu, Eric Tannier, and Steéphane Vialette

in Combinatorics of Genome Rearrangements

Published in print:
2009
Published Online:
August 2013
ISBN:
9780262062824
eISBN:
9780262258753
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262062824.003.0006
Subject:
Mathematics, Mathematical Biology

This chapter demonstrates the expansion of genome rearrangement problems to a wide mathematical field, including long-standing problems in algebra. It discusses simple permutations and the ... More


Open Problems

Guillaume Fertin, Anthony Labarre, Irena Rusu, Eric Tannier, and Steéphane Vialette

in Combinatorics of Genome Rearrangements

Published in print:
2009
Published Online:
August 2013
ISBN:
9780262062824
eISBN:
9780262258753
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262062824.003.0016
Subject:
Mathematics, Mathematical Biology

The variety of genome rearrangement problems is huge and is increasing every year. While it is possible to design many other variants that have yet to be studied, among the most studied variants, ... 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


Examples and Counterexamples

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/9780198826941.003.0017
Subject:
Mathematics, Probability / Statistics

In this chapter we further comment on the sharpness of several results presented in this monograph, by presenting examples and counterexamples. We study first the moment properties of the renewal ... More


Gaussian Approximation under Asymptotic Negative Dependence

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/9780198826941.003.0009
Subject:
Mathematics, Probability / Statistics

Here we introduce the notion of asymptotic weakly associated dependence conditions, the practical applications of which will be discussed in the next chapter. The theoretical importance of this class ... More


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