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Propriétés asymptotiques de la distribution d'un échantillon dans le cas d'un plan de sondage informatif

Abstract : Consider informative selection of a sample from a finite population. Responses are realized as iid random variables with a probability density function (pdf) f, referred to as the superpopulation model. A limit sample pdf, when population and sample sizes grow to infinity, is defined. The selection is informative in the sense that the sample responses, given that they were selected, are not iid f . The informative selection mechanism may induce dependence among the selected observations. An asymptotic framework and weak conditions on the informative selection mechanism are developed under which the empirical cdf converges uniformly and we compute the rate of convergence of the kernel density estimator to the limit sample pdf. When weak conditions on the selection are satisfied, one can consider that the responses are iid in order to make inference on a parametric population distribution. For example, we can define an approximated likelihood derived as the product of limit sample pdf's and compute a maximum sample likelihood estimator of the population parameter. Convergence and asymptotic normality of this estimator is established. The last part of the dissertation deals with balanced sampling. Consider a sampling design balanced on a set of design variables z, which may depend on the inclusion probabilities. The variance of the Horvitz Thompson estimator of the total of a study variable y can be approximated by a function of y, z, and the inclusion probabilities. We propose algorithms that compute the inclusion probabilities that minimize this approximate variance.
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Submitted on : Wednesday, January 11, 2012 - 5:07:09 PM
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  • HAL Id : tel-00658990, version 1


Daniel Bonnéry. Propriétés asymptotiques de la distribution d'un échantillon dans le cas d'un plan de sondage informatif. Statistiques [math.ST]. Université Rennes 1, 2011. Français. ⟨NNT : 2011REN1S100⟩. ⟨tel-00658990⟩



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