A Glivenko-Cantelli Bootstrap Theorem for the Foster-Greer-Thorbecke Poverty Index

A Glivenko-Cantelli Bootstrap Theorem for the Foster-Greer-Thorbecke Poverty Index

Abstract: We assume the Foster-Greer-Thorbecke (FGT) poverty index as an empirical process indexed by a particular Glivenko-Cantelli class or collection of functions and define this poverty index as a functional empirical process of the bootstrap type, to show that the outer almost sure convergence of the FGT empirical process is a necessary and sufficient condition for the outer almost sure convergence of the FGT bootstrap empirical process; that is: both processes are asymptotically equivalent respect to this type of convergence.

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Main Authors: Harmath,Pedro A., Ramoni-Perazzi,Josefa, Monsalve-Cobis,Abelardo
Format: Digital revista
Language:English
Published: Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas 2020
Online Access:http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262020000200161
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spelling oai:scielo:S0034-742620200002001612021-03-08A Glivenko-Cantelli Bootstrap Theorem for the Foster-Greer-Thorbecke Poverty IndexHarmath,Pedro A.Ramoni-Perazzi,JosefaMonsalve-Cobis,Abelardo Foster-Greer-Thorbecke poverty index convergence of empirical processes Glivenko-Cantelli classes bootstrap empirical processes Abstract: We assume the Foster-Greer-Thorbecke (FGT) poverty index as an empirical process indexed by a particular Glivenko-Cantelli class or collection of functions and define this poverty index as a functional empirical process of the bootstrap type, to show that the outer almost sure convergence of the FGT empirical process is a necessary and sufficient condition for the outer almost sure convergence of the FGT bootstrap empirical process; that is: both processes are asymptotically equivalent respect to this type of convergence.info:eu-repo/semantics/openAccessUniversidad Nacional de Colombia y Sociedad Colombiana de MatemáticasRevista Colombiana de Matemáticas v.54 n.2 20202020-12-01info:eu-repo/semantics/articletext/htmlhttp://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262020000200161en10.15446/recolma.v54n2.93845
institution SCIELO
collection OJS
country Colombia
countrycode CO
component Revista
access En linea
databasecode rev-scielo-co
tag revista
region America del Sur
libraryname SciELO
language English
format Digital
author Harmath,Pedro A.
Ramoni-Perazzi,Josefa
Monsalve-Cobis,Abelardo
spellingShingle Harmath,Pedro A.
Ramoni-Perazzi,Josefa
Monsalve-Cobis,Abelardo
A Glivenko-Cantelli Bootstrap Theorem for the Foster-Greer-Thorbecke Poverty Index
author_facet Harmath,Pedro A.
Ramoni-Perazzi,Josefa
Monsalve-Cobis,Abelardo
author_sort Harmath,Pedro A.
title A Glivenko-Cantelli Bootstrap Theorem for the Foster-Greer-Thorbecke Poverty Index
title_short A Glivenko-Cantelli Bootstrap Theorem for the Foster-Greer-Thorbecke Poverty Index
title_full A Glivenko-Cantelli Bootstrap Theorem for the Foster-Greer-Thorbecke Poverty Index
title_fullStr A Glivenko-Cantelli Bootstrap Theorem for the Foster-Greer-Thorbecke Poverty Index
title_full_unstemmed A Glivenko-Cantelli Bootstrap Theorem for the Foster-Greer-Thorbecke Poverty Index
title_sort glivenko-cantelli bootstrap theorem for the foster-greer-thorbecke poverty index
description Abstract: We assume the Foster-Greer-Thorbecke (FGT) poverty index as an empirical process indexed by a particular Glivenko-Cantelli class or collection of functions and define this poverty index as a functional empirical process of the bootstrap type, to show that the outer almost sure convergence of the FGT empirical process is a necessary and sufficient condition for the outer almost sure convergence of the FGT bootstrap empirical process; that is: both processes are asymptotically equivalent respect to this type of convergence.
publisher Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas
publishDate 2020
url http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262020000200161
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