Open AccessA Glivenko-Cantelli Bootstrap Theorem for the Foster-Greer-Thorbecke Poverty Index
Author(s) -
Pedro Harmath,
Josefá Ramoni Perazzi,
Abelardo Monsalve-Cobis
Publication year - 2021
Publication title -
revista colombiana de matemáticas/revista colombiana de matematicas
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.176
H-Index - 7
eISSN - 2357-4100
pISSN - 0034-7426
DOI - 10.15446/recolma.v54n2.93845
Subject(s) - mathematics , index (typography) , convergence (economics) , poverty , class (philosophy) , process (computing) , econometrics , economics , computer science , economic growth , artificial intelligence , world wide web , operating system
.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.