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313553

Weighted Approximations for Some Integrated Empirical Processes

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Last updated: 05 Jan 2025

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Abstract

We prove strong and weighted approximations for some newly-defined integrated empirical (IE) processes. Suitable weight functions are incorporated to show the convergence of these processes to their ideal Gaussian processes in the weighted sup-metrics. At first, the approximations were done assuming the processes are constructed from sample with fixed size. Then we derived the approximations from a randomly stopped version of those processes.  

DOI

10.21608/esju.2005.313553

Keywords

Integrated Empirical Function, Asymptotic Theory, Strong Approximations, Gaussian Processes, Weighted Sup, NORM, Tied, Down Processes, Randomly Stopped Processes

Volume

49

Article Issue

1

Related Issue

42993

Issue Date

2005-06-01

Publish Date

2005-06-01

Page Start

19

Page End

37

Print ISSN

0542-1748

Online ISSN

2786-0086

Link

https://esju.journals.ekb.eg/article_313553.html

Detail API

https://esju.journals.ekb.eg/service?article_code=313553

Order

2

Type

Original Article

Type Code

1,914

Publication Type

Journal

Publication Title

The Egyptian Statistical Journal

Publication Link

https://esju.journals.ekb.eg/

MainTitle

Weighted Approximations for Some Integrated Empirical Processes

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Article

Created At

28 Dec 2024