Uniform Convergence of the Non-Weighted Poverty Measures

Abstract

We consider in this note the weak convergence, in the frame of the empirical processes theory, of the nonweighted poverty measures viewed as stochastic processes defined on some space of bounded functions and indexed by real numbers or monotone functions. The results include the asymptotic behavior of the Foster–Greer–Thorbecke process of poverty indices. We use them to follow up the poverty evolution in poor countries between two periods with appropriate curves.

Keywords:

• Donsker's and Glivenko-Cantelli's classes
• Entropy numbers
• Poverty measures
• Weak convergence in metric spaces
• Weak convergence of empirical processes

Mathematics Subject Classification:

• Primary 2E20, 62E17, 62G30, 91B82
• Secondary 60G15, 60G70