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Estimation non-paramétrique et convergence faible des mesures de pauvreté

Abstract : 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
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Cheikh Tidiane Seck. Estimation non-paramétrique et convergence faible des mesures de pauvreté. Statistiques [math.ST]. Université Pierre et Marie Curie - Paris VI, 2011. Français. ⟨NNT : 2011PA066053⟩. ⟨tel-00825389⟩



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