Contributions à l'inférence statistique en présence de censure multivariée

Abstract : The main purpose of this thesis is to explore several approaches for studying multivariate censored data: nonparametric estimation of the joint distribution function, modeling dependence with copulas and k-clustering for the exploratory analysis. Chapter 1 presents the general framework and the contributions of this thesis. Chapter 2 deals with the estimation of the joint distribution function of two censored variables in a simplified survival model in which the difference between two censoring variables is observed. We provide a new nonparametric estimator of the joint distribution function and we establish the asymptotic normality of the integrals with respect to its associated measure. Chapter 3 is devoted to nonparametric copula estimation under bivariate censoring. We provide a discrete and two smooth copula estimators along with two estimators of its density. The discrete estimator can be seen as an extension of the empirical copula under censoring. Chapter 4 provides a new exploratory approach for censored data analysis. We consider a multivariate configuration with one variable subjected to censoring and the others completely observed. We extend the probabilistic k-quantization method in the case of random vector with one censored component. The definitions of the empirical distortion and of empirically optimal quantizer are generalized in presence of one-dimensional censoring. We study the asymptotic properties of the distortion of the empirically optimal quantizer and we provide a non-asymptotic exponential bound for the rate of convergence. Our results are then applied to construct a new two-step clustering algorithm for censored data.
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Submitted on : Tuesday, November 4, 2014 - 12:56:23 PM
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Svetlana Gribkova. Contributions à l'inférence statistique en présence de censure multivariée. Statistiques [math.ST]. Université Pierre et Marie Curie - Paris VI, 2014. Français. ⟨NNT : 2014PA066178⟩. ⟨tel-01075674v2⟩



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