Uniform weak convergence of the time-dependent poverty measures for continuous longitudinal data

Abstract

The poverty analysis may require the observation of the same set of households over the time in order to explain the evolution of the poverty situation and to try to explain their behavior. In this case, the poverty measures have to be determined continuously in some interval [0, T] and the sample poverty index becomes time-dependent. In this paper, we settle the global problem of the weak convergence of the time-dependent poverty measures in the functional space of continuous functions defined on [0, T]. We entirely describe the uniform asymptotic normality of the class of nonweighted poverty indices including the Foster–Greer–Thorbecke and Chakravarty ones, which both have the special property of satisfying all the needed axioms for a poverty index.