ABOUT THE BOOTSTRAP WEAK CONVERGENCE FOR THE FOSTER-GREER-THORBECKE POVERTY INDEX

Abstract

We assume the Foster-Greer-Thorbecke (F GT ) poverty index as a centered and normalized empirical process indexed by a particular Donsker class or collection of functions and define this poverty index as a bootstrapped empirical process, to show that the weak convergence of the F GT empirical process centered and normalized is a necessary and sufficient condition for the weak convergence of the F GT bootstrap empirical process centered and normalized. Thus, this result reflects that under certain conditions, the consistency in weak convergence of the F GT empirical process considered as a classical estimator of poverty (statistics) and the consistency in weak convergence of the F GT bootstrap empirical process considered as a bootstrap estimator of poverty (bootstrap statistics) are asymptotically equivalents for random samples of incomes statistically large and representative of a statistical universe of households.