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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Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas
2020
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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 |
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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 |
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http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262020000200161 |
work_keys_str_mv |
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