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A Glivenko-Cantelli Bootstrap Theorem for the Foster-Greer-Thorbecke Poverty Index
Un Teorema Glivenko-Cantelli Bootstrap para la Medida de Pobreza de Foster-Greer-Thorbecke
DOI:
https://doi.org/10.15446/recolma.v54n2.93845Palabras clave:
Foster-Greer-Thorbecke poverty index, convergence of empirical processes, Glivenko-Cantelli classes, bootstrap empirical processes (en)Indicador de pobreza de Foster-Greer-Thorbecke, convergencia de procesos empíricos, clases Glivenko-Cantelli, procesos empíricos bootstrap (es)
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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.
Asumimos el indicador de pobreza de Foster-Greer-Thorbe\-cke (FGT) como un proceso empírico indexado por una particular clase o colección de funciones Glivenko-Cantelli y definimos este indicador de pobreza como un proceso empírico funcional del tipo bootstrap, para probar que la convergencia casi segura exterior del proceso empírico FGT es una condición necesaria y suficiente para la convergencia casi segura exterior del proceso empírico bootstrap FGT; esto es: ambos procesos son asintóticamente equivalentes respecto de este tipo de convergencia.
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