Contribution à l'estimation non paramétrique des quantiles géométriques et à l'analyse des données fonctionnelles

Abstract : In this dissertation we study the nonparametric geometric quantile estimation, conditional geometric quantiles estimation and functional data analysis. First, we are interested to the definition of geometric quantiles. Different simulations show that Transformation-Retransformation technique should be used to estimate geometric quantiles when the distribution is not spheric. A real study shows that, data are better modelized by geometric quantiles than by marginal one's, especially when variables that make up the random vector are correlated. Then we estimate geometric quantiles when data are obtained by survey sampling techniques. First, we propose an unbaised estimator, then using linearization techniques we give its asymptotic variance. Further, we proove the consistensy of the Horvitz-Thompson estimator of the variance. Conditional geometric quantile estimation is also studied when data are dependent realisations. We prove that the proposed estimator converge uniformly on every compact sets. The second part of this thesis is devoded to the study of the Functional Principal Components Analysis parameters when data are curves selected with survey sampling techniques. Linearization techniques using influence functions allows us to give estimators of asymptotic variances. Under suitable conditions, we prove that the proposed estimators are consistent.
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Mohamed Chaouch. Contribution à l'estimation non paramétrique des quantiles géométriques et à l'analyse des données fonctionnelles. Mathématiques [math]. Université de Bourgogne, 2008. Français. ⟨tel-00364538⟩

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