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Tillé, Yves
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Tillé, Yves
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yves.tille@unine.ch
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Voici les éléments 1 - 10 sur 18
- PublicationMétadonnées seulementBias Robustness and Efficiency in Model-Based Inference(2012-9-4)
; In model-based inference, the selection of balanced samples has been considered to give protection against misspecification of the model. A recent development in finite population sampling is that balanced samples can be randomly selected. There are several possible strategies that use balanced samples. We give a definition of balanced sample that embodies overbalanced, mean-balanced, and $\pi$-balanced samples, and we derive strategies in order to equalize a $d$-weighted estimator with the best linear unbiased estimator. We show the value of selecting a balanced sample with inclusion probabilities proportional to the standard deviations of the errors with the Horvitz-Thompson estimator. This is a strategy that is design-robust and efficient. We show its superiority compared to other strategies that use balanced samples in the model-based framework. In particular, we show that this strategy is preferable to the use of overbalanced samples in the polynomial model. The problem of bias-robustness is also discussed, and we show how overspecifying the model can protect against misspecification. - PublicationMétadonnées seulementTirages coordonnés d'échantillons poissoniens(Paris: Dunod, 2011)
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- PublicationMétadonnées seulementGeneral framework for the rotation of units in repeated survey sampling(2009-3-23)
; ; Coordination of probabilistic samples is a challenging theoretical problem faced by statistical institutes. One of their aims is to obtain good estimates for each wave while spreading the response burden across the entire population. There is a collection of existing solutions that try to attend to these needs. These solutions, which were developed independently, are integrated in a general framework and their corresponding longitudinal designs are computed. The properties of these longitudinal designs are discussed. It is also noted that there is an antagonism between a good rotation and control over the cross-sectional sampling design. A compromise needs to be reached between the quality of the sample coordination, which appears to be optimal for a systematic longitudinal sampling design, and the freedom of choice of the cross-sectional design. In order to reach such a compromise, an algorithm that uses a new method of longitudinal sampling is proposed. - PublicationMétadonnées seulementTirages coordonnés d'échantillons à entropie maximale(Neuchâtel Université de Neuchâtel, 2009-3-14)
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- PublicationAccès libreEvaluation and development of strategies for sample coordination and statistical inference in finite population sampling(2009)
; Cette thèse de doctorat se concentre sur deux sujets importants de la théorie des sondages. La première partie traite du problème du fondement de l'inférence statistique en populations finies. La seconde partie traite de la question de la coordination d'échantillons dans le temps. La thèse est basée sur quatre articles, dont trois ont été déjà publiés dans des revues internationales et le quatrième a été soumis pour publication. Dans les premières chapitres de la thèse, on discute de l'optimalité de stratégies composées d'un plan d'échantillonnage et d'un estimateur. On démontre que la stratégie qui consiste à utiliser l'échantillonnage équilibré avec des probabilités proportionnelles aux erreurs du modèle linéaire, et l'estimateur de Horvitz-Thompson est optimale sous le plan et sous le modèle. En suite, on montre que cette stratégie est toujours robuste et efficace dans le cas où le modèle s'avère faux en prenant un exemple sous le modèle polynomial. Les dernières chapitres traitent un premier temps de la coordination d'échantillons stratifiés, des méthodes existante dont on compare la qualité de coordination et l'optimalité à l'aide d'une étude de simulation. On propose de nouvelles méthodes basées sur des microstrates et on teste, à nouveau par simulations, leur validité. Enfin, on a réalisé une étude plus fondamentale de l'échantillonnage répété dans le temps. On y présente les plans longitudinaux les plus connus. On note qu'il y a un antagonisme entre une bonne coordination et le choix libre d'un plan transversal. On propose également une nouvelle méthode qui peut remédier à ce problème., This Ph.D. thesis concentrates on two important subjects in survey sampling theory. One is the problem of the foundation for statistical inference in finite population sampling, and the other is the problem of coordination of samples over time. The thesis is based on four articles. Three of them are already published and the last one is submitted for publication. First, we show that the model-based and design-based inferences can be reconciliated if we search for an optimal strategy rather than just an optimal estimator, a strategy being a pair composed of a sampling design and an estimator. If we accept the idea that balanced samples are randomly selected, e.g. by the cube method, then we show that, under the linear model, an optimal strategy consists of a balanced sampling design with inclusion probabilities that are proportional to the standard deviations of the errors of the model and the Horvitz-Thompson estimator. Moreover, if the heteroscedasticity of the model is "fully explainable" by the auxiliary variables, then the best linear unbiased estimator and the Horvitz-Thompson estimator are equal. We construct a single estimator for both the design and model variance. The inference can thus be valid under the sampling design and under the model. Finally, we show that this strategy is robust and efficient when the model is misspecified. Coordination of probabilistic samples is a challenging theoretical problem faced by statistical institutes. One of their aims is to maximize or minimize the overlap between several samples drawn successively in a population that changes over time. In order to do that, a dependence between the samples must be introduced. Several methods for coordinating stratified samples have already been developed. Using simulations, we compare their optimality and quality of coordination. We present new methods based on Permanent Random Numbers (PRNs) and microstrata which have the advantage of allowing us to choose between positive or negative coordination with each of the previous samples. Simulations are run to test the validity of each of them. Another aim of sampling coordination is to obtain good estimates for each wave while spreading the response burden across the entire population. We review the existing solutions. We compute their corresponding longitudinal designs and discuss their properties. We note that there is an antagonism between a good rotation and control over the cross-sectional sampling design. In order to reach a compromise between the quality of coordination and the freedom of choice of the cross-sectional design, we propose an algorithm that uses a new method of longitudinal sampling. - PublicationMétadonnées seulement
- PublicationMétadonnées seulementSampling Procedures for Coordinating Stratified Samples: Methods Based on Microstrata(2008-3-23)
; ; The aim of sampling coordination is to maximize or minimize the overlap between several samples drawn successively in a population that changes over time. Therefore, the selection of a new sample will depend on the samples previously drawn. In order to obtain a larger (or smaller) overlap of the samples than the one obtained by independent selection of samples, a dependence between the samples must be introduced. This dependence will emphasize (or limit) the number of common units in the selected samples. Several methods for coordinating stratified samples, such as the Kish & Scott method, the Cotton & Hesse method, and the Rivière method, have already been developed. Using simulations, we compare the optimality of these methods and their quality of coordination. We present six new methods based on permanent random numbers (PRNs) and microstrata. These new methods have the advantage of allowing us to choose between positive or negative coordination with each of the previous samples. Simulations are run to test the validity of each of them.