Abstract

HARMATH, Pedro A.; RAMONI-PERAZZI, Josefa  and  MONSALVE-COBIS, Abelardo. A Glivenko-Cantelli Bootstrap Theorem for the Foster-Greer-Thorbecke Poverty Index. Rev.colomb.mat. [online]. 2020, vol.54, n.2, pp.161-179.  Epub Mar 05, 2021. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v54n2.93845.

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.

Keywords : Foster-Greer-Thorbecke poverty index; convergence of empirical processes; Glivenko-Cantelli classes; bootstrap empirical processes.

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