Robustness and outlier deyection in inferential statistics

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This thesis is structured around three main lines of research. The first focuses on the study of survival models, encompassing both non-parametric estimation of the survival function and parametric estimation under the frequentist and Bayesian approaches. The second part addresses the problem of outlier detection through the use of discordance tests. The core of this thesis, however, is devoted to the issue of Bayesian robustness. On the one hand, we study the loss robustness using a global robustness measure such as the range of the posterior expected loss function. On the other hand, we investigate the prior robustness by analysing the local curvature of the general .- divergence measure between two posterior distributions. This work extends existing results and constitutes an original contribution, leading to a theorem that provides an explicit and generalised analytical formula for the local curvature of the ..divergence, which can be computed under less restrictive constraints.

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