This dissertation first presents a general representation of poverty measures that concerns all uni-dimensional poverty measures based on the income distribution. We then, deals with two types of estimators of this general poverty index : a kernel one and a plug-in one, and analyze their asymptotic properties. Our methodology, essentially based on the modern theory of empirical processes indexed by functions, offers a general and rigorous framework, which allows to study in the same approach, the asymptotic behaviour of all the income-based poverty measures that are still available yet in the literature. We obtain the strong and uniform consistency of a very broad class of poverty measures including almost all the poverty indices proposed by economists, both decomposable and non-decomposable. This result applies for building simultaneous and accurate asymptotic confidence bands for the theoritical poverty index . A uniform functional central limit theorem is also established for this wide class of poverty measures. As a consequence, robust statistical inference procedures, based upon the covariance structure, are developped using a Wald test, in order to compare in a non-ambiguous manner two different populations in terms of poverty
Non-parametric estimation and weak convergence of poverty measures