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Moment Inequalities and Gaussian Approximation for Mixing Sequences

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/9780198826941.003.0006
Subject:
Mathematics, Probability / Statistics

Although the “mixing assumption” is nowadays considered as a rather restrictive condition, it is a powerful tool, which possesses strong properties such as preservation under functional transform, ... More


Application to the Uniform Laws of Large Numbers for Dependent 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/9780198826941.003.0016
Subject:
Mathematics, Probability / Statistics

As mentioned in Chapter 5, one of the most powerful techniques to derive limit theorems for partial sums associated with a sequence of random variables which is mixing in some sense is the coupling ... More


Functional Gaussian Approximation for Dependent Structures

Florence Merlevède, Magda Peligrad, and Sergey Utev

Published in print:
2019
Published Online:
April 2019
ISBN:
9780198826941
eISBN:
9780191865961
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198826941.001.0001
Subject:
Mathematics, Probability / Statistics

This book has its origin in the need for developing and analyzing mathematical models for phenomena that evolve in time and influence each another, and aims at a better understanding of the structure ... 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


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